Question 1

Find u - v.? $\mathbf { u } = - 3 \mathbf { i } + 2 \mathbf { j } , \mathbf { v } = 4 \mathbf { j }$ ?

Accepted Answer

A) ? $- 2 \mathbf { i } - 2 \mathbf { j }$ 
B) ? $- 3 \mathbf { i } - 2 \mathbf { j }$. 
C) ? $- 2 \mathbf { i } - 2 \mathbf { j }$. 
D) ? $2 \mathbf { i } - 2 \mathbf { j }$. 
E) ? $\mathrm { i } - \mathrm { j }$ 
A) ? $- 2 \mathbf { i } - 2 \mathbf { j }$ 
B) ? $- 3 \mathbf { i } - 2 \mathbf { j }$. 
C) ? $- 2 \mathbf { i } - 2 \mathbf { j }$. 
D) ? $2 \mathbf { i } - 2 \mathbf { j }$. 
E) ? $\mathrm { i } - \mathrm { j }$ B

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) ? $\| \mathbf { v } \| = 6 \sqrt { 3 }$ A

Question 3

Let w be a vector with initial point (4,-4)and terminal point (2,5).Write w as a linear combination of the standard unit vectors i and j.

Accepted Answer

A) ? $\mathbf { w } = 8 \mathbf { i } - 3 \mathbf { j }$ 
B) ? $\mathbf { w } = 0 \mathbf { i } + 3 \mathbf { j }$ 
C) ? $\mathbf { w } = \mathbf { i } + 6 \mathbf { j }$ 
D) ? $\mathbf { w } = - 2 \mathbf { i } + 9 \mathbf { j }$ 
E) ? $\mathbf { w } = 6 \mathbf { i } - 9 \mathbf { j }$ 
A) ? $\mathbf { w } = 8 \mathbf { i } - 3 \mathbf { j }$ 
B) ? $\mathbf { w } = 0 \mathbf { i } + 3 \mathbf { j }$ 
C) ? $\mathbf { w } = \mathbf { i } + 6 \mathbf { j }$ 
D) ? $\mathbf { w } = - 2 \mathbf { i } + 9 \mathbf { j }$ 
E) ? $\mathbf { w } = 6 \mathbf { i } - 9 \mathbf { j }$ D

Question 4

Find a unit vector in the direction of the given vector. ?? $\mathbf { u } = \langle 4,0 \rangle$ ?

Accepted Answer

A)  $\langle 1,1 \rangle$ 
B)  $\langle 1,0 \rangle$ 
C)  $\langle 0,0 \rangle$ 
D)  $\langle 4,0 \rangle$ 
E)  $\langle 0,1 \rangle$ 
A)  $\langle 1,1 \rangle$ 
B)  $\langle 1,0 \rangle$ 
C)  $\langle 0,0 \rangle$ 
D)  $\langle 4,0 \rangle$ 
E)  $\langle 0,1 \rangle$

Question 5

A traffic light weighing 15 pounds is suspended by two cables (see figure).Find the tension in each cable if θ1 = 40° and θ2 = 35°.Approximate the answers to one decimal place.​   ​

Accepted Answer

A) ​​TL = 12.7 lb;TR = 12.7 lb 
B) ​TL = 11.9 lb;TR = 11.9 lb 
C) ​TL = 11.9 lb;TR = 12.7 lb 
D) TL = 12.7 lb;TR = 11.9 lb 
E) ​​TL = 13.7 lb;TR = 12.9 lb 
A) ​​TL = 12.7 lb;TR = 12.7 lb 
B) ​TL = 11.9 lb;TR = 11.9 lb 
C) ​TL = 11.9 lb;TR = 12.7 lb 
D) TL = 12.7 lb;TR = 11.9 lb 
E) ​​TL = 13.7 lb;TR = 12.9 lb

Question 6

A gun with a muzzle velocity of 1700 feet per second is fired at an angle of 4° above the horizontal.Find the vertical and horizontal components of the velocity.(Round your answer to one decimal place. ) ​

Accepted Answer

A) Vertical ≈ 118.6 ft/sec,Horisontal ≈ 1,695.9 ft/sec. 
B) ​Vertical ≈ 119.6 ft/sec,Horisontal ≈ 1,696.9 ft/sec. 
C) ​Vertical ≈ 1,695.9 ft/sec,Horisontal ≈ 1,695.9 ft/sec. 
D) ​Vertical ≈ 1,695.9 ft/sec,Horisontal ≈ 118.6 ft/sec. 
E) ​Vertical ≈ 118.6 ft/sec,Horisontal ≈ 118.6 ft/sec. 
A) Vertical ≈ 118.6 ft/sec,Horisontal ≈ 1,695.9 ft/sec. 
B) ​Vertical ≈ 119.6 ft/sec,Horisontal ≈ 1,696.9 ft/sec. 
C) ​Vertical ≈ 1,695.9 ft/sec,Horisontal ≈ 1,695.9 ft/sec. 
D) ​Vertical ≈ 1,695.9 ft/sec,Horisontal ≈ 118.6 ft/sec. 
E) ​Vertical ≈ 118.6 ft/sec,Horisontal ≈ 118.6 ft/sec.

Question 7

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 8

Find u + v.? $\mathbf { u } = \langle 6,1 \rangle , \mathbf { v } = \langle 1,7 \rangle$ ?

Accepted Answer

A) ? $\langle 8,9 \rangle$ 
B)  $\langle 7,8 \rangle$ 
C) ? $\langle 8,8 \rangle$ 
D) ? $\langle 8,7 \rangle$ 
E) ? $\langle 7,7 \rangle$ 
A) ? $\langle 8,9 \rangle$ 
B)  $\langle 7,8 \rangle$ 
C) ? $\langle 8,8 \rangle$ 
D) ? $\langle 8,7 \rangle$ 
E) ? $\langle 7,7 \rangle$

Question 9

Find a unit vector in the direction of the given vector.? $\mathbf { u } = \langle 0 , - 4 \rangle$ ?

Accepted Answer

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

Question 10

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. ?
Magnitude
Angle $\| \mathbf { v } \| = 6$ $45 ^ { \circ }$ ?

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 11

?Find the magnitude of vector v with initial point (7,5)and terminal point (-3,-5). ?

Accepted Answer

A) ? $10 \sqrt { 2 }$ 
B) ?14 
C) ? $20 \sqrt { 2 }$ 
D) ? $\sqrt { 74 }$ 
E) ? $2 \sqrt { 51 }$ 
A) ? $10 \sqrt { 2 }$ 
B) ?14 
C) ? $20 \sqrt { 2 }$ 
D) ? $\sqrt { 74 }$ 
E) ? $2 \sqrt { 51 }$

Question 12

Detroit Tigers pitcher Joel Zumaya was recorded throwing a pitch at a velocity of 107 miles per hour.If he threw the pitch at an angle of 32° below the horizontal,find the vertical and horizontal components of the velocity.(Round your answers to one decimal place. ) ​

Accepted Answer

A) Vertical ≈ -55.7 mi/h,Horisontal ≈ 91.7 mi/h. 
B) Vertical ≈ 90.7 mi/h,Horisontal ≈ -56.7 mi/h. 
C) Vertical ≈ -56.7 mi/h,Horisontal ≈ -56.7 mi/h. 
D) Vertical ≈ -56.7 mi/h,Horisontal ≈ 90.7 mi/h. 
E) Vertical ≈ 90.7 mi/h,Horisontal ≈ 90.7 mi/h. 
A) Vertical ≈ -55.7 mi/h,Horisontal ≈ 91.7 mi/h. 
B) Vertical ≈ 90.7 mi/h,Horisontal ≈ -56.7 mi/h. 
C) Vertical ≈ -56.7 mi/h,Horisontal ≈ -56.7 mi/h. 
D) Vertical ≈ -56.7 mi/h,Horisontal ≈ 90.7 mi/h. 
E) Vertical ≈ 90.7 mi/h,Horisontal ≈ 90.7 mi/h.

Question 13

Find 2u - 3v.? $\mathbf { u } = 4 \mathbf { i } , \mathbf { v } = 5 \mathbf { j }$ ?

Accepted Answer

A) ? $15 \mathbf { i } - 8 \mathbf { j }$ 
B)  $4 \mathbf { i } - 5 \mathbf { j }$ 
C)  $- 8 \mathbf { i } - 15 \mathbf { j }$ ? 
D)  $8 \mathbf { i } - 15 \mathbf { j }$ 
E)  $8 \mathbf { i } + 15 \mathbf { j }$ ? 
A) ? $15 \mathbf { i } - 8 \mathbf { j }$ 
B)  $4 \mathbf { i } - 5 \mathbf { j }$ 
C)  $- 8 \mathbf { i } - 15 \mathbf { j }$ ? 
D)  $8 \mathbf { i } - 15 \mathbf { j }$ 
E)  $8 \mathbf { i } + 15 \mathbf { j }$ ?

Question 14

Find a unit vector in the direction of the given vector.? $\mathbf { w } = 5 \mathbf { j }$ ?

Accepted Answer

A) j 
B) i 
C) - j 
D) - i 
E) ?i - j 
A) j 
B) i 
C) - j 
D) - i 
E) ?i - j

Question 15

The initial and terminal points of vector v are (3,-8)and (7,1),respectively.Select v in component form. ?

Accepted Answer

A) ? $\mathbf { v } = \langle - 4 , - 9 \rangle$ 
B) ? $\mathbf { v } = \langle - 4,9 \rangle$ 
C)  $\mathbf { v } = \langle 4,9 \rangle$ 
D)  $\mathbf { v } = \langle 4 , - 9 \rangle$ 
E) ? $\mathbf { v } = \langle 9,4 \rangle$ 
A) ? $\mathbf { v } = \langle - 4 , - 9 \rangle$ 
B) ? $\mathbf { v } = \langle - 4,9 \rangle$ 
C)  $\mathbf { v } = \langle 4,9 \rangle$ 
D)  $\mathbf { v } = \langle 4 , - 9 \rangle$ 
E) ? $\mathbf { v } = \langle 9,4 \rangle$

Question 16

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 F if W = 100 pounds and θ = 11°.Approximate the answer to one decimal place.
​

Accepted Answer

A) 18.1 lb 
B) 21.1 lb 
C) 19.1 lb 
D) 20.1 lb 
E) 17.1 lb 
A) 18.1 lb 
B) 21.1 lb 
C) 19.1 lb 
D) 20.1 lb 
E) 17.1 lb

Question 17

Find a unit vector in the direction of the given vector.? $\mathbf { v } = 2 \mathbf { i } + 2 \mathbf { j }$ ?

Accepted Answer

A) ? $- \frac { \sqrt { 2 } } { 2 } \mathbf { i } - \frac { \sqrt { 2 } } { 2 } j$ 
B) ? $- \frac { \sqrt { 2 } } { 2 } \mathbf { i } + \frac { \sqrt { 2 } } { 2 } j$ 
C) ? $\frac { \sqrt { 2 } } { 2 } \mathbf { i } - \frac { \sqrt { 2 } } { 2 } \mathbf { j }$ 
D) ? $\sqrt { 2 } \mathbf { i } + \sqrt { 2 } \mathbf { j }$ 
E)  $\frac { \sqrt { 2 } } { 2 } \mathbf { i } + \frac { \sqrt { 2 } } { 2 } \mathbf { j }$ 
A) ? $- \frac { \sqrt { 2 } } { 2 } \mathbf { i } - \frac { \sqrt { 2 } } { 2 } j$ 
B) ? $- \frac { \sqrt { 2 } } { 2 } \mathbf { i } + \frac { \sqrt { 2 } } { 2 } j$ 
C) ? $\frac { \sqrt { 2 } } { 2 } \mathbf { i } - \frac { \sqrt { 2 } } { 2 } \mathbf { j }$ 
D) ? $\sqrt { 2 } \mathbf { i } + \sqrt { 2 } \mathbf { j }$ 
E)  $\frac { \sqrt { 2 } } { 2 } \mathbf { i } + \frac { \sqrt { 2 } } { 2 } \mathbf { j }$

Question 18

Find the component form of vector v with initial point (1,-7)and terminal point (-3,1).

Accepted Answer

A) ? $\mathbf { v } = \langle - 4 , - 8 \rangle$ 
B)  $\mathbf { v } = \langle - 4,8 \rangle$ 
C) ? $v = \langle 8 , - 4 \rangle$ 
D) ? $v = \langle 0 , - 4 \rangle$ 
E) ? $\mathbf { v } = \langle - 8 , - 4 \rangle$ 
A) ? $\mathbf { v } = \langle - 4 , - 8 \rangle$ 
B)  $\mathbf { v } = \langle - 4,8 \rangle$ 
C) ? $v = \langle 8 , - 4 \rangle$ 
D) ? $v = \langle 0 , - 4 \rangle$ 
E) ? $\mathbf { v } = \langle - 8 , - 4 \rangle$

Question 19

Find the component form of v if $\| \mathbf { v } \| = 8$ and the angle it makes with the x-axis is 60°.

Accepted Answer

A) ? $\langle 4 \sqrt { 3 } , 4 \rangle$ 
B) ? $\langle 8,8 \sqrt { 3 } \rangle$ 
C)  $\langle 4,4 \sqrt { 3 } \rangle$ 
D) ? $\langle 8 \sqrt { 3 } , 8 \rangle$ 
E) ? $\langle 4 \sqrt { 2 } , 4 \sqrt { 2 } \rangle$ 
A) ? $\langle 4 \sqrt { 3 } , 4 \rangle$ 
B) ? $\langle 8,8 \sqrt { 3 } \rangle$ 
C)  $\langle 4,4 \sqrt { 3 } \rangle$ 
D) ? $\langle 8 \sqrt { 3 } , 8 \rangle$ 
E) ? $\langle 4 \sqrt { 2 } , 4 \sqrt { 2 } \rangle$

Question 20

Given $$\mathbf { u } = \langle 3 , - 2 \rangle$$ and $\mathbf { v } = \langle - 3,2 \rangle$ ,determine $- 4 \mathbf { u } - \mathbf { v }$ .

Accepted Answer

A) ? $$- 4 \mathbf { u } - \mathbf { v } = \langle 9 , - 14 \rangle$$ 
B)  $- 4 \mathbf { u } - \mathbf { v } = \langle - 9,6 \rangle$ 
C) ? $- 4 \mathbf { u } - \mathbf { v } = \langle - 14 , - 14 \rangle$ 
D) ? $- 4 \mathbf { u } - \mathbf { v } = \langle 11 , - 14 \rangle$ 
E) ? $- 4 \mathbf { u } - \mathbf { v } = \langle - 11,10 \rangle$ 
A) ? $$- 4 \mathbf { u } - \mathbf { v } = \langle 9 , - 14 \rangle$$ 
B)  $- 4 \mathbf { u } - \mathbf { v } = \langle - 9,6 \rangle$ 
C) ? $- 4 \mathbf { u } - \mathbf { v } = \langle - 14 , - 14 \rangle$ 
D) ? $- 4 \mathbf { u } - \mathbf { v } = \langle 11 , - 14 \rangle$ 
E) ? $- 4 \mathbf { u } - \mathbf { v } = \langle - 11,10 \rangle$

Exam 38:Vectors in the Plane

Find u - v.? u=−3i+2j,v=4j\mathbf { u } = - 3 \mathbf { i } + 2 \mathbf { j } , \mathbf { v } = 4 \mathbf { j }u=−3i+2j,v=4j ?

Find the magnitude of vector v.?

Let w be a vector with initial point (4,-4)and terminal point (2,5).Write w as a linear combination of the standard unit vectors i and j.

Find a unit vector in the direction of the given vector. ?? u=⟨4,0⟩\mathbf { u } = \langle 4,0 \rangleu=⟨4,0⟩ ?

A traffic light weighing 15 pounds is suspended by two cables (see figure).Find the tension in each cable if θ1 = 40° and θ2 = 35°.Approximate the answers to one decimal place.​ ​

A gun with a muzzle velocity of 1700 feet per second is fired at an angle of 4° above the horizontal.Find the vertical and horizontal components of the velocity.(Round your answer to one decimal place. ) ​

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 u + v.? u=⟨6,1⟩,v=⟨1,7⟩\mathbf { u } = \langle 6,1 \rangle , \mathbf { v } = \langle 1,7 \rangleu=⟨6,1⟩,v=⟨1,7⟩ ?

Find a unit vector in the direction of the given vector.? u=⟨0,−4⟩\mathbf { u } = \langle 0 , - 4 \rangleu=⟨0,−4⟩ ?

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. ? Magnitude Angle ∥v∥=6\| \mathbf { v } \| = 6∥v∥=6 45∘45 ^ { \circ }45∘ ?

?Find the magnitude of vector v with initial point (7,5)and terminal point (-3,-5). ?

Detroit Tigers pitcher Joel Zumaya was recorded throwing a pitch at a velocity of 107 miles per hour.If he threw the pitch at an angle of 32° below the horizontal,find the vertical and horizontal components of the velocity.(Round your answers to one decimal place. ) ​

Find 2u - 3v.? u=4i,v=5j\mathbf { u } = 4 \mathbf { i } , \mathbf { v } = 5 \mathbf { j }u=4i,v=5j ?

Find a unit vector in the direction of the given vector.? w=5j\mathbf { w } = 5 \mathbf { j }w=5j ?

The initial and terminal points of vector v are (3,-8)and (7,1),respectively.Select v in component form. ?

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 F if W = 100 pounds and θ = 11°.Approximate the answer to one decimal place. ​

Find a unit vector in the direction of the given vector.? v=2i+2j\mathbf { v } = 2 \mathbf { i } + 2 \mathbf { j }v=2i+2j ?

Find the component form of vector v with initial point (1,-7)and terminal point (-3,1).

Find the component form of v if ∥v∥=8\| \mathbf { v } \| = 8∥v∥=8 and the angle it makes with the x-axis is 60°.

Given u=⟨3,−2⟩\mathbf { u } = \langle 3 , - 2 \rangleu=⟨3,−2⟩ and v=⟨−3,2⟩\mathbf { v } = \langle - 3,2 \ranglev=⟨−3,2⟩ ,determine −4u−v- 4 \mathbf { u } - \mathbf { v }−4u−v .

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Find u - v.? $\mathbf { u } = - 3 \mathbf { i } + 2 \mathbf { j } , \mathbf { v } = 4 \mathbf { j }$ ?

Find a unit vector in the direction of the given vector. ?? $\mathbf { u } = \langle 4,0 \rangle$ ?

A traffic light weighing 15 pounds is suspended by two cables (see figure).Find the tension in each cable if θ₁ = 40° and θ₂ = 35°.Approximate the answers to one decimal place.

A gun with a muzzle velocity of 1700 feet per second is fired at an angle of 4° above the horizontal.Find the vertical and horizontal components of the velocity.(Round your answer to one decimal place. )

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 u + v.? $\mathbf { u } = \langle 6,1 \rangle , \mathbf { v } = \langle 1,7 \rangle$ ?

Find a unit vector in the direction of the given vector.? $\mathbf { u } = \langle 0 , - 4 \rangle$ ?

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. ? Magnitude Angle $\| \mathbf { v } \| = 6$ $45 ^ { \circ }$ ?

Detroit Tigers pitcher Joel Zumaya was recorded throwing a pitch at a velocity of 107 miles per hour.If he threw the pitch at an angle of 32° below the horizontal,find the vertical and horizontal components of the velocity.(Round your answers to one decimal place. )

Find 2u - 3v.? $\mathbf { u } = 4 \mathbf { i } , \mathbf { v } = 5 \mathbf { j }$ ?

Find a unit vector in the direction of the given vector.? $\mathbf { w } = 5 \mathbf { j }$ ?

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 F if W = 100 pounds and θ = 11°.Approximate the answer to one decimal place.

Find a unit vector in the direction of the given vector.? $\mathbf { v } = 2 \mathbf { i } + 2 \mathbf { j }$ ?

Find the component form of v if $\| \mathbf { v } \| = 8$ and the angle it makes with the x-axis is 60°.

Given $\mathbf { u } = \langle 3 , - 2 \rangle$ and $\mathbf { v } = \langle - 3,2 \rangle$ ,determine $- 4 \mathbf { u } - \mathbf { v }$ .