Question 1

Use the dot product to find the magnitude of u if $\mathbf { u } = - 5 \mathbf { i } - 2 \mathbf { j }$

Accepted Answer

A)  $\| \mathbf { u } \| =$ 10 
B)  $\| \mathbf { u } \| =$ $2 \sqrt { 29 }$ 
C)  $\| \mathbf { u } \| = 7$ 
D)  $\| \mathbf { u } \| = 15$ 
E)  $\| \mathbf { u } \| =$ $\sqrt { 29 }$ 
A)  $\| \mathbf { u } \| =$ 10 
B)  $\| \mathbf { u } \| =$ $2 \sqrt { 29 }$ 
C)  $\| \mathbf { u } \| = 7$ 
D)  $\| \mathbf { u } \| = 15$ 
E)  $\| \mathbf { u } \| =$ $\sqrt { 29 }$

Question 2

Find the magnitude of vector v.

Accepted Answer

A)  $\| \mathbf { v } \| = 5$ 
B)   $\| \mathbf { v } \| = 2 \sqrt { 7 }$ 
C)   $\| \mathbf { v } \| = 6$ 
D)   $\| \mathbf { v } \| = 4 \sqrt { 2 }$ 
E)   $\| \mathbf { v } \| = 6 \sqrt { 3 }$ 
A)  $\| \mathbf { v } \| = 5$ 
B)   $\| \mathbf { v } \| = 2 \sqrt { 7 }$ 
C)   $\| \mathbf { v } \| = 6$ 
D)   $\| \mathbf { v } \| = 4 \sqrt { 2 }$ 
E)   $\| \mathbf { v } \| = 6 \sqrt { 3 }$

Question 3

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. ​
A = 23°, a = 3, b = 17
​

Accepted Answer

A) Law of Sines; No solution 
B) Law of Cosines; No solution 
C) Law of Cosines; c ≈ 3, B ≈ 43°, C ≈ 114° 
D) Law of Cosines; c ≈ 6, B ≈ 43°, C ≈ 114° 
E) Law of Sines; c ≈ 17, B ≈ 114°, C ≈ 43° 
A) Law of Sines; No solution 
B) Law of Cosines; No solution 
C) Law of Cosines; c ≈ 3, B ≈ 43°, C ≈ 114° 
D) Law of Cosines; c ≈ 6, B ≈ 43°, C ≈ 114° 
E) Law of Sines; c ≈ 17, B ≈ 114°, C ≈ 43°

Question 4

Represent the complex number graphically, and find the trigonometric form of the number.  
4

Accepted Answer

A)     $4 ( \cos 0 + i \sin 0 )$ 
B)     $4 ( \cos 4 + i \sin 4 )$ 
C)     $4 ( \cos 4 - i \sin 4 )$ 
D)    $4 ( \cos 0 - i \sin 0 )$ 
E)    $4 ( \cos 4 - i \sin 4 )$ 
A)     $4 ( \cos 0 + i \sin 0 )$ 
B)     $4 ( \cos 4 + i \sin 4 )$ 
C)     $4 ( \cos 4 - i \sin 4 )$ 
D)    $4 ( \cos 0 - i \sin 0 )$ 
E)    $4 ( \cos 4 - i \sin 4 )$

Question 5

Find the trigonometric form of the complex number represented graphically.

Accepted Answer

A) 3 $\sqrt { 2 }$ (cos(3$\pi $/4) + isin(3$\pi $/4)) 
B) -3(cos(7$\pi $/4) + isin(7$\pi $/4)) 
C) 3 $\sqrt { 2 }$ (cos(7$\pi $/4) + isin(7$\pi $/4)) 
D) -3 $\sqrt { 2 }$ (cos(3$\pi $/4) + isin(3$\pi $/4)) 
E)  3 $\sqrt { 2 }$ (cos(5$\pi $/4) + isin(5$\pi $/4)) 
A) 3 $\sqrt { 2 }$ (cos(3$\pi $/4) + isin(3$\pi $/4)) 
B) -3(cos(7$\pi $/4) + isin(7$\pi $/4)) 
C) 3 $\sqrt { 2 }$ (cos(7$\pi $/4) + isin(7$\pi $/4)) 
D) -3 $\sqrt { 2 }$ (cos(3$\pi $/4) + isin(3$\pi $/4)) 
E)  3 $\sqrt { 2 }$ (cos(5$\pi $/4) + isin(5$\pi $/4))

Question 6

Find the trigonometric form of the complex number shown below.   $- 3 + 4 i$

Accepted Answer

A)   $\sqrt { 25 }$ (cos (arctan (- $\frac { 1 } { 6 }$ )) + i sin (arctan (- $\frac { 1 } { 6 }$ ))) 
B)   $\sqrt { 25 }$ (cos (arctan ( $\frac { 4 } { 5 }$ )) + i sin (arctan ( $\frac { 4 } { 5 }$ ))) 
C)   $\sqrt { 25 }$ (cos (arctan (- $\frac { 4 } { 3 }$ )) + i sin (arctan (- $\frac { 4 } { 3 }$ ))) 
D)   $\sqrt { 25 }$ (cos (arctan (- $\frac { 2 } { 3 }$ )) + i sin (arctan (- $\frac { 2 } { 3 }$ ))) 
E)   $\sqrt { 25 }$ (cos (arctan (4)) + i sin (arctan (4))) 
A)   $\sqrt { 25 }$ (cos (arctan (- $\frac { 1 } { 6 }$ )) + i sin (arctan (- $\frac { 1 } { 6 }$ ))) 
B)   $\sqrt { 25 }$ (cos (arctan ( $\frac { 4 } { 5 }$ )) + i sin (arctan ( $\frac { 4 } { 5 }$ ))) 
C)   $\sqrt { 25 }$ (cos (arctan (- $\frac { 4 } { 3 }$ )) + i sin (arctan (- $\frac { 4 } { 3 }$ ))) 
D)   $\sqrt { 25 }$ (cos (arctan (- $\frac { 2 } { 3 }$ )) + i sin (arctan (- $\frac { 2 } { 3 }$ ))) 
E)   $\sqrt { 25 }$ (cos (arctan (4)) + i sin (arctan (4)))

Question 7

Perform the operation and leave the result in trigonometric form.   $\frac { 16 \left( \cos 98 ^ { \circ } + i \sin 98 ^ { \circ } \right) } { 2 \left( \cos 128 ^ { \circ } + i \sin 128 ^ { \circ } \right) }$

Accepted Answer

A)  $8 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$ 
B)   $8 \left( \cos 98 ^ { \circ } - i \sin 98 ^ { \circ } \right)$ 
C)   $8 \left( \cos 128 ^ { \circ } + i \sin 128 ^ { \circ } \right)$ 
D)   $8 \left( \cos 330 ^ { \circ } - i \sin 330 ^ { \circ } \right)$ 
E)   $8 \left( \cos 98 ^ { \circ } + i \sin 98 ^ { \circ } \right)$ 
A)  $8 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$ 
B)   $8 \left( \cos 98 ^ { \circ } - i \sin 98 ^ { \circ } \right)$ 
C)   $8 \left( \cos 128 ^ { \circ } + i \sin 128 ^ { \circ } \right)$ 
D)   $8 \left( \cos 330 ^ { \circ } - i \sin 330 ^ { \circ } \right)$ 
E)   $8 \left( \cos 98 ^ { \circ } + i \sin 98 ^ { \circ } \right)$

Question 8

After a severe storm, three sisters, April, May, and June, stood on their front porch and noticed that the tree in their front yard was leaning 3° from vertical toward the house.From the porch, which is 96 feet away from the base of the tree, they noticed that the angle of elevation to the top of the tree was 31°.Approximate the height of the tree.Round answer to two decimal places. ​

Accepted Answer

A) 61.76 feet 
B) 69.64 feet 
C) 56 feet 
D) 59.13 feet 
E) 59.64 feet 
A) 61.76 feet 
B) 69.64 feet 
C) 56 feet 
D) 59.13 feet 
E) 59.64 feet

Question 9

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal place. ​
A = 13.22, b = 9.36, c = 15.95
​

Accepted Answer

A) 35.77 
B) ​14.09 
C) ​79.16 
D) ​61.84 
E) ​48.31 
A) 35.77 
B) ​14.09 
C) ​79.16 
D) ​61.84 
E) ​48.31

Question 10

Find the product $( 6 + 6 i ) ( 2 - 2 i )$ using trigonometric forms.Leave the result in trigonometric form.

Accepted Answer

A)  $12 \left( \cos \left( 45 ^ { \circ } \right) + i \sin \left( 45 ^ { \circ } \right) \right)$ 
B)  $12 \left( \cos \left( 0 ^ { \circ } \right) + i \sin \left( 0 ^ { \circ } \right) \right)$ 
C)  $24 \left( \cos \left( - 45 ^ { \circ } \right) + i \sin \left( - 45 ^ { \circ } \right) \right)$ 
D)  $24 \left( \cos \left( 45 ^ { \circ } \right) + i \sin \left( 45 ^ { \circ } \right) \right)$ 
E)  $24 \left( \cos \left( 0 ^ { \circ } \right) + i \sin \left( 0 ^ { \circ } \right) \right)$ 
A)  $12 \left( \cos \left( 45 ^ { \circ } \right) + i \sin \left( 45 ^ { \circ } \right) \right)$ 
B)  $12 \left( \cos \left( 0 ^ { \circ } \right) + i \sin \left( 0 ^ { \circ } \right) \right)$ 
C)  $24 \left( \cos \left( - 45 ^ { \circ } \right) + i \sin \left( - 45 ^ { \circ } \right) \right)$ 
D)  $24 \left( \cos \left( 45 ^ { \circ } \right) + i \sin \left( 45 ^ { \circ } \right) \right)$ 
E)  $24 \left( \cos \left( 0 ^ { \circ } \right) + i \sin \left( 0 ^ { \circ } \right) \right)$

Question 11

Find all solutions to the following equation. $x ^ { 3 } - 216 = 0$

Accepted Answer

A)   $x = 6,6 + 6 i \sqrt { 3 } , 6 - 6 i \sqrt { 3 }$ 
B)  $x = 6,3 - 3 i \sqrt { 3 } , - 3 - 3 i \sqrt { 3 }$ 
C)   $x = 6 , - 3 - 3 i \sqrt { 3 } , - 3 + 3 i \sqrt { 3 }$ 
D)  $x = - 6 i$ 
E)  $x = - 6$ 
A)   $x = 6,6 + 6 i \sqrt { 3 } , 6 - 6 i \sqrt { 3 }$ 
B)  $x = 6,3 - 3 i \sqrt { 3 } , - 3 - 3 i \sqrt { 3 }$ 
C)   $x = 6 , - 3 - 3 i \sqrt { 3 } , - 3 + 3 i \sqrt { 3 }$ 
D)  $x = - 6 i$ 
E)  $x = - 6$

Question 12

Find the angle between the vectors u and v if $\mathbf { u } = \mathbf { i } + 2 \mathbf { j }$ and $\mathbf { v } = 4 \mathbf { i } + 2 \mathbf { j }$ Round answer to two decimal places.

Accepted Answer

A) 36.87° 
B) 37.83° 
C) 38.28° 
D) 34.94° 
E) 35.63° 
A) 36.87° 
B) 37.83° 
C) 38.28° 
D) 34.94° 
E) 35.63°

Question 13

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. ​
A = 35°, B = 60°, c = 10
​

Accepted Answer

A) C = 85°, a ​≈ 6.76, b ≈ 8.69 
B) C = 85°, a ​≈ 8.69, b ≈ 9.69 
C) C = 85°, a ​≈ 8.76, b ≈ 10.69 
D) C = 85°, a ​≈ 5.76, b ≈ 8.69 
E) ​C = 85°, a ​≈ 7.76, b ≈ 10.69 
A) C = 85°, a ​≈ 6.76, b ≈ 8.69 
B) C = 85°, a ​≈ 8.69, b ≈ 9.69 
C) C = 85°, a ​≈ 8.76, b ≈ 10.69 
D) C = 85°, a ​≈ 5.76, b ≈ 8.69 
E) ​C = 85°, a ​≈ 7.76, b ≈ 10.69

Question 14

Find a unit vector in the direction of the given vector.   $\mathbf { u } = \langle - 6,6 \rangle$

Accepted Answer

A)  $\langle 0,0 \rangle$ 
B)   $\left\langle - \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right\rangle$ 
C)   $\left\langle - \frac { \sqrt { 2 } } { 2 } , - \frac { \sqrt { 2 } } { 2 } \right\rangle$ 
D)   $\left\langle \frac { \sqrt { 2 } } { 2 } , - \frac { \sqrt { 2 } } { 2 } \right\rangle$ 
E)   $\left\langle \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right\rangle$ 
A)  $\langle 0,0 \rangle$ 
B)   $\left\langle - \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right\rangle$ 
C)   $\left\langle - \frac { \sqrt { 2 } } { 2 } , - \frac { \sqrt { 2 } } { 2 } \right\rangle$ 
D)   $\left\langle \frac { \sqrt { 2 } } { 2 } , - \frac { \sqrt { 2 } } { 2 } \right\rangle$ 
E)   $\left\langle \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right\rangle$

Question 15

Find the component form of v if $\| \mathbf { v } \| = 10$ and the angle it makes with the x-axis is 120°.

Accepted Answer

A)   $\langle - 5 \sqrt { 3 } , 5 \rangle$ 
B)   $\langle - 5 \sqrt { 3 } , - 10 \rangle$ 
C)   $\langle - 5 \sqrt { 2 } , 5 \sqrt { 2 } \rangle$ 
D)   $\langle - 5,5 \sqrt { 3 } \rangle$ 
E)   $\langle - 10,10 \sqrt { 3 } \rangle$ 
A)   $\langle - 5 \sqrt { 3 } , 5 \rangle$ 
B)   $\langle - 5 \sqrt { 3 } , - 10 \rangle$ 
C)   $\langle - 5 \sqrt { 2 } , 5 \sqrt { 2 } \rangle$ 
D)   $\langle - 5,5 \sqrt { 3 } \rangle$ 
E)   $\langle - 10,10 \sqrt { 3 } \rangle$

Question 16

Use DeMoivre's Theorem to find the indicated power of the following complex number. $\left[ - 2 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right) \right] ^ { 6 }$

Accepted Answer

A) -4 
B) -8 
C)  $64 + 64 \sqrt { 3 }$ 
D)  $32 + 32 \sqrt { 3 }$ 
E) 8 
A) -4 
B) -8 
C)  $64 + 64 \sqrt { 3 }$ 
D)  $32 + 32 \sqrt { 3 }$ 
E) 8

Question 17

Find u - v. 
$\mathbf { u } = \langle 0,0 \rangle , \mathbf { v } = \langle 2,1 \rangle$

Accepted Answer

A)   $\langle - 1 , - 2 \rangle$ 
B)   $\langle - 1 , - 1 \rangle$ 
C)  $\langle - 2 , - 1 \rangle$ 
D)   $\langle - 2 , - 2 \rangle$ 
E)   $\langle - 1,0 \rangle$ 
A)   $\langle - 1 , - 2 \rangle$ 
B)   $\langle - 1 , - 1 \rangle$ 
C)  $\langle - 2 , - 1 \rangle$ 
D)   $\langle - 2 , - 2 \rangle$ 
E)   $\langle - 1,0 \rangle$

Question 18

Determine whether u are v and orthogonal, parallel, or neither. $\mathbf { u } = \left\langle \frac { 1 } { 3 } , \frac { 5 } { 2 } \right\rangle$ , $\mathbf { v } = \langle - 4 , - 30 \rangle$

Accepted Answer

A) orthogonal 
B) parallel 
C) neither 
A) orthogonal 
B) parallel 
C) neither

Question 19

Use vectors to find the measure of the angle at vertex B of triangle ABC, when $A = ( 5,4 )$ , $B = ( - 2,4 )$ , and $C = ( - 3 , - 4 )$ .Round answer to two decimal places.

Accepted Answer

A) 95.94° 
B) 98.47° 
C) 97.13° 
D) 95.04° 
E) 99.65° 
A) 95.94° 
B) 98.47° 
C) 97.13° 
D) 95.04° 
E) 99.65°

Question 20

Use the vectors $\mathbf { u } = \langle 4,5 \rangle$ , $\mathbf { v } = \langle - 6,5 \rangle$ , and $\mathbf { w } = \langle 6 , - 4 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar.
  $\langle \mathbf { u } \cdot \mathbf { v } \rangle - \langle \mathbf { u } \cdot \mathbf { w } \rangle$

Accepted Answer

A) -1; scalar 
B)  $\langle 1 , - 7 \rangle$ ; vector 
C)  $\langle - 3 , - 3 \rangle$ ; vector 
D) -3; scalar 
E) -5; scalar 
A) -1; scalar 
B)  $\langle 1 , - 7 \rangle$ ; vector 
C)  $\langle - 3 , - 3 \rangle$ ; vector 
D) -3; scalar 
E) -5; scalar

Use the dot product to find the magnitude of u if $\mathbf { u } = - 5 \mathbf { i } - 2 \mathbf { j }$

Find the magnitude of vector v.

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. A = 23°, a = 3, b = 17

Represent the complex number graphically, and find the trigonometric form of the number. 4

Find the trigonometric form of the complex number represented graphically.

Find the trigonometric form of the complex number shown below. $- 3 + 4 i$

Perform the operation and leave the result in trigonometric form. $\frac { 16 \left( \cos 98 ^ { \circ } + i \sin 98 ^ { \circ } \right) } { 2 \left( \cos 128 ^ { \circ } + i \sin 128 ^ { \circ } \right) }$

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal place. A = 13.22, b = 9.36, c = 15.95

Find the product $( 6 + 6 i ) ( 2 - 2 i )$ using trigonometric forms.Leave the result in trigonometric form.

Find all solutions to the following equation. $x ^ { 3 } - 216 = 0$

Find the angle between the vectors u and v if $\mathbf { u } = \mathbf { i } + 2 \mathbf { j }$ and $\mathbf { v } = 4 \mathbf { i } + 2 \mathbf { j }$ Round answer to two decimal places.

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. A = 35°, B = 60°, c = 10

Find a unit vector in the direction of the given vector. $\mathbf { u } = \langle - 6,6 \rangle$

Find the component form of v if $\| \mathbf { v } \| = 10$ and the angle it makes with the x-axis is 120°.

Use DeMoivre's Theorem to find the indicated power of the following complex number. $\left[ - 2 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right) \right] ^ { 6 }$

Find u - v. $\mathbf { u } = \langle 0,0 \rangle , \mathbf { v } = \langle 2,1 \rangle$

Determine whether u are v and orthogonal, parallel, or neither. $\mathbf { u } = \left\langle \frac { 1 } { 3 } , \frac { 5 } { 2 } \right\rangle$ , $\mathbf { v } = \langle - 4 , - 30 \rangle$

Use vectors to find the measure of the angle at vertex B of triangle ABC, when $A = ( 5,4 )$ , $B = ( - 2,4 )$ , and $C = ( - 3 , - 4 )$ .Round answer to two decimal places.

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

Exam 6: Additional Topics In Trigonometery

Use the dot product to find the magnitude of u if u=−5i−2j\mathbf { u } = - 5 \mathbf { i } - 2 \mathbf { j }u=−5i−2j

Find the magnitude of vector v.

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. ​ A = 23°, a = 3, b = 17 ​

Represent the complex number graphically, and find the trigonometric form of the number. 4

Find the trigonometric form of the complex number represented graphically.

Find the trigonometric form of the complex number shown below. −3+4i- 3 + 4 i−3+4i

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal place. ​ A = 13.22, b = 9.36, c = 15.95 ​

Find the product (6+6i)(2−2i)( 6 + 6 i ) ( 2 - 2 i )(6+6i)(2−2i) using trigonometric forms.Leave the result in trigonometric form.

Find all solutions to the following equation. x3−216=0x ^ { 3 } - 216 = 0x3−216=0

Find the angle between the vectors u and v if u=i+2j\mathbf { u } = \mathbf { i } + 2 \mathbf { j }u=i+2j and v=4i+2j\mathbf { v } = 4 \mathbf { i } + 2 \mathbf { j }v=4i+2j Round answer to two decimal places.

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. ​ A = 35°, B = 60°, c = 10 ​

Find a unit vector in the direction of the given vector. u=⟨−6,6⟩\mathbf { u } = \langle - 6,6 \rangleu=⟨−6,6⟩

Find the component form of v if ∥v∥=10\| \mathbf { v } \| = 10∥v∥=10 and the angle it makes with the x-axis is 120°.

Use DeMoivre's Theorem to find the indicated power of the following complex number. [−2(cos⁡π3+isin⁡π3)]6\left[ - 2 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right) \right] ^ { 6 }[−2(cos3π​+isin3π​)]6

Find u - v. u=⟨0,0⟩,v=⟨2,1⟩\mathbf { u } = \langle 0,0 \rangle , \mathbf { v } = \langle 2,1 \rangleu=⟨0,0⟩,v=⟨2,1⟩

Determine whether u are v and orthogonal, parallel, or neither. u=⟨13,52⟩\mathbf { u } = \left\langle \frac { 1 } { 3 } , \frac { 5 } { 2 } \right\rangleu=⟨31​,25​⟩ , v=⟨−4,−30⟩\mathbf { v } = \langle - 4 , - 30 \ranglev=⟨−4,−30⟩

Use vectors to find the measure of the angle at vertex B of triangle ABC, when A=(5,4)A = ( 5,4 )A=(5,4) , B=(−2,4)B = ( - 2,4 )B=(−2,4) , and C=(−3,−4)C = ( - 3 , - 4 )C=(−3,−4) .Round answer to two decimal places.

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 dot product to find the magnitude of u if $\mathbf { u } = - 5 \mathbf { i } - 2 \mathbf { j }$

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. A = 23°, a = 3, b = 17

Find the trigonometric form of the complex number shown below. $- 3 + 4 i$

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal place. A = 13.22, b = 9.36, c = 15.95

Find the product $( 6 + 6 i ) ( 2 - 2 i )$ using trigonometric forms.Leave the result in trigonometric form.

Find all solutions to the following equation. $x ^ { 3 } - 216 = 0$

Find the angle between the vectors u and v if $\mathbf { u } = \mathbf { i } + 2 \mathbf { j }$ and $\mathbf { v } = 4 \mathbf { i } + 2 \mathbf { j }$ Round answer to two decimal places.

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. A = 35°, B = 60°, c = 10

Find a unit vector in the direction of the given vector. $\mathbf { u } = \langle - 6,6 \rangle$

Find the component form of v if $\| \mathbf { v } \| = 10$ and the angle it makes with the x-axis is 120°.

Use DeMoivre's Theorem to find the indicated power of the following complex number. $\left[ - 2 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right) \right] ^ { 6 }$

Find u - v. $\mathbf { u } = \langle 0,0 \rangle , \mathbf { v } = \langle 2,1 \rangle$

Determine whether u are v and orthogonal, parallel, or neither. $\mathbf { u } = \left\langle \frac { 1 } { 3 } , \frac { 5 } { 2 } \right\rangle$ , $\mathbf { v } = \langle - 4 , - 30 \rangle$

Use vectors to find the measure of the angle at vertex B of triangle ABC, when $A = ( 5,4 )$ , $B = ( - 2,4 )$ , and $C = ( - 3 , - 4 )$ .Round answer to two decimal places.