Question 1

Find the trigonometric form of the complex number shown below. 10i

Accepted Answer

A)   $10 ( \cos \pi + i \sin \pi )$ 
B)   $10 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$ 
C)   $10 ( \cos 0 + i \sin 0 )$ 
D)   $10 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$ 
E)  $10 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
A)   $10 ( \cos \pi + i \sin \pi )$ 
B)   $10 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$ 
C)   $10 ( \cos 0 + i \sin 0 )$ 
D)   $10 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$ 
E)  $10 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$

Question 2

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. ​
A = 125°, B = 45°, c = 13
​

Accepted Answer

A) C = 10°, a ≈ 61.33, b ≈ 52.94 
B) C = 10°, a ≈ 54.94, b ≈ 62.33 
C) ​C = 10°, a ≈ 53.94, b ≈ 52.94 
D) ​C = 10°, a ≈ 64.33, b ≈ 52.94 
E) ​C = 10°, a ≈ 63.33, b ≈ 54.94 
A) C = 10°, a ≈ 61.33, b ≈ 52.94 
B) C = 10°, a ≈ 54.94, b ≈ 62.33 
C) ​C = 10°, a ≈ 53.94, b ≈ 52.94 
D) ​C = 10°, a ≈ 64.33, b ≈ 52.94 
E) ​C = 10°, a ≈ 63.33, b ≈ 54.94

Question 3

Perform the indicated operation using the standard form.   $- 6 i ( 1 + i )$

Accepted Answer

A)  $- 6 i ( 1 + i ) = 6 - 6 i$ 
B)   $- 6 i ( 1 + i ) = 12 - 6 i$ 
C)   $- 6 i ( 1 + i ) = 6 + 12 i$ 
D)   $- 6 i ( 1 + i ) = 6 - 12 i$ 
E)   $- 6 i ( 1 + i ) = 6 + 6 i$ 
A)  $- 6 i ( 1 + i ) = 6 - 6 i$ 
B)   $- 6 i ( 1 + i ) = 12 - 6 i$ 
C)   $- 6 i ( 1 + i ) = 6 + 12 i$ 
D)   $- 6 i ( 1 + i ) = 6 - 12 i$ 
E)   $- 6 i ( 1 + i ) = 6 + 6 i$

Question 4

Find the standard form of the complex number.Then represent the complex number graphically.   $7 ( \cos 0 + i \sin 0 )$

Accepted Answer

A)      7 
B)    7 
C)      -7 
D)    -7 
E) None of the above 
A)      7 
B)    7 
C)      -7 
D)    -7 
E) None of the above

Question 5

Find values for b such that the triangle has two solutions.  
A = 32°, a = 5

Accepted Answer

A)  $5 \leq b \leq \frac { 5 } { \sin 32 ^ { \circ } }$ 
B)  $5  b > \frac { 5 } { \sin 32 ^ { \circ } }$ 
A)  $5 \leq b \leq \frac { 5 } { \sin 32 ^ { \circ } }$ 
B)  $5  b > \frac { 5 } { \sin 32 ^ { \circ } }$

Question 6

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​
Find θ if F = 5,100 pounds and W = 14,000 lb.Approximate the answer to one decimal place.
​

Accepted Answer

A) 19.4° 
B) ​21.4° 
C) ​23.4° 
D) ​20.4° 
E) ​22.4° 
A) 19.4° 
B) ​21.4° 
C) ​23.4° 
D) ​20.4° 
E) ​22.4°

Question 7

Find the standard form of the complex number $5 \left( \cos \left( 25 ^ { \circ } 46 ^ { \prime } \right) + i \sin \left( 25 ^ { \circ } 46 ^ { \prime } \right) \right)$ .Round values to the nearest hundredth.

Accepted Answer

A)  $4.91 + 1.36 i$ 
B)  $4.5 + 2.17 i$ 
C)  $- 4.5 - 2.17 i$ 
D)  $- 2.81 - 2.92 i$ 
E)  $2.81 + 2.92 i$ 
A)  $4.91 + 1.36 i$ 
B)  $4.5 + 2.17 i$ 
C)  $- 4.5 - 2.17 i$ 
D)  $- 2.81 - 2.92 i$ 
E)  $2.81 + 2.92 i$

Question 8

Represent the complex number below graphically. 2 $\sqrt { 2 }$ $\left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right)$

Accepted Answer

A)     
B)    
C)     
D)     
E)     
A)     
B)    
C)     
D)     
E)

Question 9

Find the component form of v given its magnitude and the angle it makes with the positive x-axis.  
$\begin{array}{lr}\text { Magnitude}&\text { Angle }\\|\mathbf{v}\|=6&45^o
\end{array}$

Accepted Answer

A)   $\langle - 3 \sqrt { 2 } , 3 \sqrt { 2 } \rangle$ 
B)   $\langle - 3 \sqrt { 2 } , - 3 \sqrt { 2 } \rangle$ 
C)   $\langle 3,3 \rangle$ 
D)   $\langle 3 \sqrt { 2 } , 3 \sqrt { 2 } \rangle$ 
E)   $\langle 3 \sqrt { 2 } , - 3 \sqrt { 2 } \rangle$ 
A)   $\langle - 3 \sqrt { 2 } , 3 \sqrt { 2 } \rangle$ 
B)   $\langle - 3 \sqrt { 2 } , - 3 \sqrt { 2 } \rangle$ 
C)   $\langle 3,3 \rangle$ 
D)   $\langle 3 \sqrt { 2 } , 3 \sqrt { 2 } \rangle$ 
E)   $\langle 3 \sqrt { 2 } , - 3 \sqrt { 2 } \rangle$

Question 10

Use the dot product to find the magnitude of u if $\mathbf { u } = \langle 3,2 \rangle$

Accepted Answer

A)  $\| \mathbf { u } \| =$ $2 \sqrt { 13 }$ 
B)  $\| \mathbf { u } \| =$ $\sqrt { 13 }$ 
C)  $\| \mathbf { u } \| = 6$ 
D)  $\| \mathbf { u } \| = 5$ 
E)  $\| \mathbf { u } \| = 7$ 
A)  $\| \mathbf { u } \| =$ $2 \sqrt { 13 }$ 
B)  $\| \mathbf { u } \| =$ $\sqrt { 13 }$ 
C)  $\| \mathbf { u } \| = 6$ 
D)  $\| \mathbf { u } \| = 5$ 
E)  $\| \mathbf { u } \| = 7$

Question 11

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. ​
A = 51, b = 21, c = 68
​

Accepted Answer

A) A ≈ 30.37°, B ≈ 12.02°, C ≈ 137.61° 
B) A ≈ 30.37°, B ≈ 137.61°, C ≈ 12.02° 
C) A ≈ 12.02°, B ≈ 30.37°, C ≈ 137.61° 
D) A ≈ 137.61°, B ≈ 12.02°, C ≈ 30.37° 
E) A ≈ 137.61°, B ≈ 30.37°, C ≈ 12.02° 
A) A ≈ 30.37°, B ≈ 12.02°, C ≈ 137.61° 
B) A ≈ 30.37°, B ≈ 137.61°, C ≈ 12.02° 
C) A ≈ 12.02°, B ≈ 30.37°, C ≈ 137.61° 
D) A ≈ 137.61°, B ≈ 12.02°, C ≈ 30.37° 
E) A ≈ 137.61°, B ≈ 30.37°, C ≈ 12.02°

Question 12

Find the trigonometric form of the complex number shown below. $\sqrt { 3 } + i$

Accepted Answer

A)  $\sqrt { 3 } \left( \cos \left( \frac { \pi } { 2 } \right) + i \sin \left( \frac { \pi } { 2 } \right) \right)$ 
B)  $2 \left( \cos \left( \frac { \sqrt { 3 } \pi } { 2 } \right) + i \sin \left( \frac { \sqrt { 3 } \pi } { 2 } \right) \right)$ 
C)  $\sqrt { 3 } \left( \cos \left( \frac { \pi } { 3 } \right) + i \sin \left( \frac { \pi } { 3 } \right) \right)$ 
D)  $2 \left( \cos \left( \frac { \pi } { 6 } \right) + i \sin \left( \frac { \pi } { 6 } \right) \right)$ 
E)   $2 \sqrt { 3 } \left( \cos \left( \frac { \pi } { 6 } \right) + i \sin \left( \frac { \pi } { 6 } \right) \right)$ 
A)  $\sqrt { 3 } \left( \cos \left( \frac { \pi } { 2 } \right) + i \sin \left( \frac { \pi } { 2 } \right) \right)$ 
B)  $2 \left( \cos \left( \frac { \sqrt { 3 } \pi } { 2 } \right) + i \sin \left( \frac { \sqrt { 3 } \pi } { 2 } \right) \right)$ 
C)  $\sqrt { 3 } \left( \cos \left( \frac { \pi } { 3 } \right) + i \sin \left( \frac { \pi } { 3 } \right) \right)$ 
D)  $2 \left( \cos \left( \frac { \pi } { 6 } \right) + i \sin \left( \frac { \pi } { 6 } \right) \right)$ 
E)   $2 \sqrt { 3 } \left( \cos \left( \frac { \pi } { 6 } \right) + i \sin \left( \frac { \pi } { 6 } \right) \right)$

Question 13

Find the trigonometric form of - 21 - 21i.

Accepted Answer

A)  $\frac { 21 } { 2 } \left( \cos \frac { 5 \pi } { 2 } + i \sin \frac { 5 \pi } { 2 } \right)$ 
B)   $21 \left( \cos \frac { 5 \pi } { 2 } + i \sin \frac { 5 \pi } { 2 } \right)$ 
C)   $21 \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$ 
D)   $21 \sqrt { 2 } \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$ 
E)   $\frac { 441 } { 4 } \left( \cos \frac { 5 \pi } { 8 } + i \sin \frac { 5 \pi } { 8 } \right)$ 
A)  $\frac { 21 } { 2 } \left( \cos \frac { 5 \pi } { 2 } + i \sin \frac { 5 \pi } { 2 } \right)$ 
B)   $21 \left( \cos \frac { 5 \pi } { 2 } + i \sin \frac { 5 \pi } { 2 } \right)$ 
C)   $21 \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$ 
D)   $21 \sqrt { 2 } \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$ 
E)   $\frac { 441 } { 4 } \left( \cos \frac { 5 \pi } { 8 } + i \sin \frac { 5 \pi } { 8 } \right)$

Question 14

Use the vector $\mathbf { u } = \langle 3,2 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar.   $\mathbf { u } ^. { \mathbf { u } }$

Accepted Answer

A)  $\langle 13,15 \rangle$ ; vector 
B) 15; scalar 
C) 13; scalar 
D) 11; scalar 
E)  $\langle 17,9 \rangle$ ; vector 
A)  $\langle 13,15 \rangle$ ; vector 
B) 15; scalar 
C) 13; scalar 
D) 11; scalar 
E)  $\langle 17,9 \rangle$ ; vector

Question 15

Use the Law of Sines to solve (if possible) the triangle.If two solutions exist, find both.Round your answers to two decimal places. ​
A = 60°, a = 13, b = 11.6
​

Accepted Answer

A) B ≈ 69.40°, C ≈ 50.6°, c ≈ 11.6 
B) B ≈ 91°, C ≈ 29°, c ≈ 14.05 
C) B ≈ 50.6°, C ≈ 69.40°, c ≈ 14.05 
D) B ≈ 29°, C ≈ 91°, c ≈ 13 
E) No Solution 
A) B ≈ 69.40°, C ≈ 50.6°, c ≈ 11.6 
B) B ≈ 91°, C ≈ 29°, c ≈ 14.05 
C) B ≈ 50.6°, C ≈ 69.40°, c ≈ 14.05 
D) B ≈ 29°, C ≈ 91°, c ≈ 13 
E) No Solution

Question 16

Represent the complex number graphically, and find the trigonometric form of the number.  
12i

Accepted Answer

A)     $12 ( \cos \pi + i \sin \pi )$ 
B)     $12 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
C)     $12 ( \cos \pi + i \sin \pi )$ 
D)    $12 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
E)     $12 ( \cos \pi + i \sin \pi )$ 
A)     $12 ( \cos \pi + i \sin \pi )$ 
B)     $12 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
C)     $12 ( \cos \pi + i \sin \pi )$ 
D)    $12 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
E)     $12 ( \cos \pi + i \sin \pi )$

Question 17

Given $\mathbf { u } = \langle 3 , - 2 \rangle$ and $\mathbf { v } = \langle 1 , - 3 \rangle$ , find $\text { u v }$ .

Accepted Answer

A) 3 
B) -3 
C) -7 
D) 9 
E) -11 
A) 3 
B) -3 
C) -7 
D) 9 
E) -11

Question 18

Use the Heron's formula to find the area of the triangle.Round your answer upto one decimal place. ​
A = 3.2, b = 10.9, c = 9
​

Accepted Answer

A) 7.0 
B) 6.4 
C) 3.7 
D) 45.3 
E) 12.6 
A) 7.0 
B) 6.4 
C) 3.7 
D) 45.3 
E) 12.6

Question 19

Determine $\text { u v }$ if $\| \mathbf { u } \| = 5 , \| \mathbf { v } \| = 6$ , and $\theta = \frac { \pi } { 3 }$ where $\theta$ is the angle between u and v.Round answer to two decimal places.

Accepted Answer

A) 21.21 
B) 20.49 
C) 15.00 
D) 18.11 
E) 25.98 
A) 21.21 
B) 20.49 
C) 15.00 
D) 18.11 
E) 25.98

Question 20

If $\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }$ and $\mathbf { v } = - 6 \mathbf { i } + 5 \mathbf { j }$ , find $\mathbf { w } = 3 \mathbf { u } + 5 \mathbf { v }$ .

Accepted Answer

A)   $\mathbf { w } = - 39 \mathbf { i } + 43 \mathbf { j }$ 
B)   $\mathbf { w } = - 33 \mathbf { i } + 43 \mathbf { j }$ 
C)   $\mathbf { w } = - 27 \mathbf { i } + 55 \mathbf { j }$ 
D)   $\mathbf { w } = - 39 \mathbf { i } + 45 \mathbf { j }$ 
E)   $\mathbf { w } = 16 \mathbf { i } - 12 \mathbf { j }$ 
A)   $\mathbf { w } = - 39 \mathbf { i } + 43 \mathbf { j }$ 
B)   $\mathbf { w } = - 33 \mathbf { i } + 43 \mathbf { j }$ 
C)   $\mathbf { w } = - 27 \mathbf { i } + 55 \mathbf { j }$ 
D)   $\mathbf { w } = - 39 \mathbf { i } + 45 \mathbf { j }$ 
E)   $\mathbf { w } = 16 \mathbf { i } - 12 \mathbf { j }$

Find the trigonometric form of the complex number shown below. 10i

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. A = 125°, B = 45°, c = 13

Perform the indicated operation using the standard form. $- 6 i ( 1 + i )$

Find the standard form of the complex number.Then represent the complex number graphically. $7 ( \cos 0 + i \sin 0 )$

Find values for b such that the triangle has two solutions. A = 32°, a = 5

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find θ if F = 5,100 pounds and W = 14,000 lb.Approximate the answer to one decimal place.

Find the standard form of the complex number $5 \left( \cos \left( 25 ^ { \circ } 46 ^ { \prime } \right) + i \sin \left( 25 ^ { \circ } 46 ^ { \prime } \right) \right)$ .Round values to the nearest hundredth.

Represent the complex number below graphically. 2 $\sqrt { 2 }$ $\left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right)$ $Represent the complex number below graphically. 2 \sqrt { 2 } \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right)$

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. Magnitude Angle \|\|=6 4

Use the dot product to find the magnitude of u if $\mathbf { u } = \langle 3,2 \rangle$

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. A = 51, b = 21, c = 68

Find the trigonometric form of the complex number shown below. $\sqrt { 3 } + i$

Find the trigonometric form of - 21 - 21i.

Use the vector $\mathbf { u } = \langle 3,2 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar. $\mathbf { u } ^. { \mathbf { u } }$

Use the Law of Sines to solve (if possible) the triangle.If two solutions exist, find both.Round your answers to two decimal places. A = 60°, a = 13, b = 11.6

Represent the complex number graphically, and find the trigonometric form of the number. 12i

Given $\mathbf { u } = \langle 3 , - 2 \rangle$ and $\mathbf { v } = \langle 1 , - 3 \rangle$ , find $\text { u v }$ .

Use the Heron's formula to find the area of the triangle.Round your answer upto one decimal place. A = 3.2, b = 10.9, c = 9

Determine $\text { u v }$ if $\| \mathbf { u } \| = 5 , \| \mathbf { v } \| = 6$ , and $\theta = \frac { \pi } { 3 }$ where $\theta$ is the angle between u and v.Round answer to two decimal places.

If $\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }$ and $\mathbf { v } = - 6 \mathbf { i } + 5 \mathbf { j }$ , find $\mathbf { w } = 3 \mathbf { u } + 5 \mathbf { v }$ .

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

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Exam 6: Additional Topics In Trigonometery

Find the trigonometric form of the complex number shown below. 10i

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. ​ A = 125°, B = 45°, c = 13 ​

Perform the indicated operation using the standard form. −6i(1+i)- 6 i ( 1 + i )−6i(1+i)

Find the standard form of the complex number.Then represent the complex number graphically. 7(cos⁡0+isin⁡0)7 ( \cos 0 + i \sin 0 )7(cos0+isin0)

Find values for b such that the triangle has two solutions. A = 32°, a = 5

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​ Find θ if F = 5,100 pounds and W = 14,000 lb.Approximate the answer to one decimal place. ​

Find the standard form of the complex number 5(cos⁡(25∘46′)+isin⁡(25∘46′))5 \left( \cos \left( 25 ^ { \circ } 46 ^ { \prime } \right) + i \sin \left( 25 ^ { \circ } 46 ^ { \prime } \right) \right)5(cos(25∘46′)+isin(25∘46′)) .Round values to the nearest hundredth.

Represent the complex number below graphically. 2 2\sqrt { 2 }2​ (cos⁡135∘+isin⁡135∘)\left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right)(cos135∘+isin135∘)

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. Magnitude Angle \|\|=6 4

Use the dot product to find the magnitude of u if u=⟨3,2⟩\mathbf { u } = \langle 3,2 \rangleu=⟨3,2⟩

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. ​ A = 51, b = 21, c = 68 ​

Find the trigonometric form of the complex number shown below. 3+i\sqrt { 3 } + i3​+i

Find the trigonometric form of - 21 - 21i.

Use the vector u=⟨3,2⟩\mathbf { u } = \langle 3,2 \rangleu=⟨3,2⟩ to find the indicated quantity.State whether the result is a vector or a scalar. u.u\mathbf { u } ^. { \mathbf { u } }u.u

Use the Law of Sines to solve (if possible) the triangle.If two solutions exist, find both.Round your answers to two decimal places. ​ A = 60°, a = 13, b = 11.6 ​

Represent the complex number graphically, and find the trigonometric form of the number. 12i

Given u=⟨3,−2⟩\mathbf { u } = \langle 3 , - 2 \rangleu=⟨3,−2⟩ and v=⟨1,−3⟩\mathbf { v } = \langle 1 , - 3 \ranglev=⟨1,−3⟩ , find u v \text { u v } u v .

Use the Heron's formula to find the area of the triangle.Round your answer upto one decimal place. ​ A = 3.2, b = 10.9, c = 9 ​

Determine u v \text { u v } u v if ∥u∥=5,∥v∥=6\| \mathbf { u } \| = 5 , \| \mathbf { v } \| = 6∥u∥=5,∥v∥=6 , and θ=π3\theta = \frac { \pi } { 3 }θ=3π​ where θ\thetaθ is the angle between u and v.Round answer to two decimal places.

If u=−3i+6j\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }u=−3i+6j and v=−6i+5j\mathbf { v } = - 6 \mathbf { i } + 5 \mathbf { j }v=−6i+5j , find w=3u+5v\mathbf { w } = 3 \mathbf { u } + 5 \mathbf { v }w=3u+5v .

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. A = 125°, B = 45°, c = 13

Perform the indicated operation using the standard form. $- 6 i ( 1 + i )$

Find the standard form of the complex number.Then represent the complex number graphically. $7 ( \cos 0 + i \sin 0 )$

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find θ if F = 5,100 pounds and W = 14,000 lb.Approximate the answer to one decimal place.

Find the standard form of the complex number $5 \left( \cos \left( 25 ^ { \circ } 46 ^ { \prime } \right) + i \sin \left( 25 ^ { \circ } 46 ^ { \prime } \right) \right)$ .Round values to the nearest hundredth.

Represent the complex number below graphically. 2 $\sqrt { 2 }$ $\left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right)$ $Represent the complex number below graphically. 2 \sqrt { 2 } \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right)$

Use the dot product to find the magnitude of u if $\mathbf { u } = \langle 3,2 \rangle$

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. A = 51, b = 21, c = 68

Find the trigonometric form of the complex number shown below. $\sqrt { 3 } + i$

Use the vector $\mathbf { u } = \langle 3,2 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar. $\mathbf { u } ^. { \mathbf { u } }$

Use the Law of Sines to solve (if possible) the triangle.If two solutions exist, find both.Round your answers to two decimal places. A = 60°, a = 13, b = 11.6

Given $\mathbf { u } = \langle 3 , - 2 \rangle$ and $\mathbf { v } = \langle 1 , - 3 \rangle$ , find $\text { u v }$ .

Use the Heron's formula to find the area of the triangle.Round your answer upto one decimal place. A = 3.2, b = 10.9, c = 9

Determine $\text { u v }$ if $\| \mathbf { u } \| = 5 , \| \mathbf { v } \| = 6$ , and $\theta = \frac { \pi } { 3 }$ where $\theta$ is the angle between u and v.Round answer to two decimal places.

If $\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }$ and $\mathbf { v } = - 6 \mathbf { i } + 5 \mathbf { j }$ , find $\mathbf { w } = 3 \mathbf { u } + 5 \mathbf { v }$ .