Find the angle θ between the vectors. $\begin{array} { l } \mathbf { u } = \langle 6,2 \rangle \\ \mathbf { v } = \langle 7,0 \rangle \end{array}$ (Round the answer to 2 decimal places. )

A) $18.43 ^ { \circ }$ B) $33.43 ^ { \circ }$ C) $23.43 ^ { \circ }$ D) $28.43 ^ { \circ }$ E) $38.43 ^ { \circ }$ A) $18.43 ^ { \circ }$ B) $33.43 ^ { \circ }$ C) $23.43 ^ { \circ }$ D) $28.43 ^ { \circ }$ E) $38.43 ^ { \circ }$

Find the projection of u onto v. $\begin{array} { l } \mathbf { u } = \langle - 5 , - 5 \rangle \\ \mathbf { v } = \langle - 5 , - 1 \rangle \end{array}$

A) $\frac { 1 } { 13 } \langle - 75 , - 15 \rangle$ B) $13 \langle - 15 , - 75 \rangle$ C) $\frac { 1 } { 13 } \langle - 5 , - 5 \rangle$ D) $\frac { 13 } { 15 } \langle - 75 , - 15 \rangle$ E) $\frac { 15 } { 13 } \langle - 75 , - 15 \rangle$ A) $\frac { 1 } { 13 } \langle - 75 , - 15 \rangle$ B) $13 \langle - 15 , - 75 \rangle$ C) $\frac { 1 } { 13 } \langle - 5 , - 5 \rangle$ D) $\frac { 13 } { 15 } \langle - 75 , - 15 \rangle$ E) $\frac { 15 } { 13 } \langle - 75 , - 15 \rangle$

Find the projection of u onto v. $\begin{array} { l } \mathbf { u } = \langle 0,4 \rangle \\ \mathbf { v } = \langle 3,20 \rangle \end{array}$

A) $\frac { 1 } { 409 } \langle 0,3 \rangle$ B) $409 \langle 1600,240 \rangle$ C) $\frac { 80 } { 409 } \langle 240,1600 \rangle$ D) $\frac { 409 } { 80 } \langle 240,1600 \rangle$ E) $\frac { 1 } { 409 } \langle 240,1600 \rangle$ A) $\frac { 1 } { 409 } \langle 0,3 \rangle$ B) $409 \langle 1600,240 \rangle$ C) $\frac { 80 } { 409 } \langle 240,1600 \rangle$ D) $\frac { 409 } { 80 } \langle 240,1600 \rangle$ E) $\frac { 1 } { 409 } \langle 240,1600 \rangle$

Exam 39:Vectors and Dot Products

Given vectors $\mathbf { u } = \left\langle u _ { 1 } , u _ { 2 } \right\rangle$ , $\mathbf { v } = \left\langle v _ { 1 } , v _ { 2 } \right\rangle$ and $\mathbf { w } = \left\langle w _ { 1 } , w _ { 2 } \right\rangle$ determine whether the result of the following expression is a vector or a scalar. $6 w \cdot 3 w$

Free

(Multiple Choice)

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Question 1

Correct Answer:

Verified

B

Find the angle between the vectors u and v. $\mathbf { u } = \cos \left( \frac { \pi } { 3 } \right) \mathbf { i } + \sin \left( \frac { \pi } { 3 } \right) \mathbf { j }$ , $\mathbf { v } = \cos \left( \frac { 5 \pi } { 4 } \right) \mathbf { i } + \sin \left( \frac { 5 \pi } { 4 } \right) \mathbf { j }$

Free

(Multiple Choice)

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Question 2

Correct Answer:

Verified

D

Determine the work done by a crane lifting a 2,800-pound car 7 feet.

Free

(Multiple Choice)

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Question 3

Correct Answer:

Verified

A

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

(Multiple Choice)

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Question 4

Find the projection of u onto v if , $\mathbf { u } = \langle - 5 , - 4 \rangle$ , $\mathbf { v } = \langle 2 , - 5 \rangle$ .

(Multiple Choice)

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Question 5

The vector $\mathbf { u } = \langle 3900,4000 \rangle$ gives the number of units of two models of laptops produced by a company.The vector $\mathbf { u } = \langle 1450,1000 \rangle$ gives the prices (in dollars)of the two models of laptops,respectively.Identify the vector operation used to increase revenue by 6%.

(Multiple Choice)

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Question 6

Use vectors to find the measure of the angle at vertex B of triangle ABC,when $A = ( 5,1 )$ , $B = ( - 5,1 )$ ,and $C = ( - 3 , - 5 )$ .Round answer to two decimal places.

(Multiple Choice)

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Question 7

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

(Multiple Choice)

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Question 8

Use the dot product to find the magnitude of u if $\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }$

(Multiple Choice)

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Question 9

Determine whether u are v and orthogonal,parallel,or neither. $\mathbf { u } = \left\langle \frac { - 4 } { 3 } , \frac { 3 } { 2 } \right\rangle , \mathbf { v } = \langle 16 , - 18 \rangle$

(Multiple Choice)

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Question 10

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

(Multiple Choice)

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Question 11

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

(Multiple Choice)

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Question 12

A force of 45 pounds is exerted along a rope attached to a crate at an angle of 30° above the horizontal.The crate is moved 31 feet horizontally.How much work has been accomplished? Round your answer to one decimal place.

(Multiple Choice)

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Question 13

Find the angle θ between the vectors. =\langle6,2\rangle =\langle7,0\rangle (Round the answer to 2 decimal places. )

(Multiple Choice)

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Question 14

Find the projection of u onto v. =\langle-5,-5\rangle =\langle-5,-1\rangle

(Multiple Choice)

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Question 15

Find the projection of u onto v.Then write u as the sum of two orthogonal vectors,one of which is $\operatorname { proj } _ { \mathrm { v } } \mathbf { u }$ . $\mathbf { u } = \langle 30,5 \rangle$ $\mathbf { v } = \langle 1 , - 6 \rangle$

(Multiple Choice)

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Question 16

Find the projection of u onto v. =\langle0,4\rangle =\langle3,20\rangle

(Multiple Choice)

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Question 17

Find the angle between the vectors u and v if $\mathbf { u } = 3 \mathbf { i } - 2 \mathbf { j }$ and $\mathbf { u } = 3 \mathbf { i } + 2 \mathbf { j }$ Round your answer to two decimal places.

(Multiple Choice)

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Question 18

Use the vectors $\mathbf { u } = \langle 2,4 \rangle$ , $\mathbf { v } = \langle - 5,3 \rangle$ and $\mathbf { w } = \langle 3 , - 1 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar. $\left( \mathbf { v } ^ { . } \mathbf { u } \right) - \left( \mathbf { w } ^ { . } \mathbf { v } \right)$

(Multiple Choice)

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Question 19

Given vectors $\mathbf { u } = \langle - 1,3 \rangle$ and $\mathbf { v } = \langle 1,4 \rangle$ determine the quantity indicated below. $- 2 \mathbf { u }{ \cdot}- 4 \mathbf { v }$

(Multiple Choice)

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Question 20

Exam 39:Vectors and Dot Products

Determine the work done by a crane lifting a 2,800-pound car 7 feet.

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{.}\mathbf { u } ^ { }u.u ​

​Find the projection of u onto v if , u=⟨−5,−4⟩\mathbf { u } = \langle - 5 , - 4 \rangleu=⟨−5,−4⟩ , v=⟨2,−5⟩\mathbf { v } = \langle 2 , - 5 \ranglev=⟨2,−5⟩ .

Use vectors to find the measure of the angle at vertex B of triangle ABC,when A=(5,1)A = ( 5,1 )A=(5,1) , B=(−5,1)B = ( - 5,1 )B=(−5,1) ,and C=(−3,−5)C = ( - 3 , - 5 )C=(−3,−5) .Round answer to two decimal places.

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⋅vu\cdot vu⋅v .

Use the dot product to find the magnitude of u if u=−3i+6j\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }u=−3i+6j

Determine whether u are v and orthogonal,parallel,or neither. u=⟨−43,32⟩,v=⟨16,−18⟩\mathbf { u } = \left\langle \frac { - 4 } { 3 } , \frac { 3 } { 2 } \right\rangle , \mathbf { v } = \langle 16 , - 18 \rangleu=⟨3−4​,23​⟩,v=⟨16,−18⟩

Determine u.vu^.vu.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 is the angle between u and v.Round answer to two decimal places.

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⟩

A force of 45 pounds is exerted along a rope attached to a crate at an angle of 30° above the horizontal.The crate is moved 31 feet horizontally.How much work has been accomplished? Round your answer to one decimal place.

Find the angle θ between the vectors.​ =\langle6,2\rangle =\langle7,0\rangle ​ (Round the answer to 2 decimal places. ) ​

Find the projection of u onto v.​ =\langle-5,-5\rangle =\langle-5,-1\rangle ​

Find the projection of u onto v.​ =\langle0,4\rangle =\langle3,20\rangle ​

Find the angle between the vectors u and v if u=3i−2j\mathbf { u } = 3 \mathbf { i } - 2 \mathbf { j }u=3i−2j and u=3i+2j\mathbf { u } = 3 \mathbf { i } + 2 \mathbf { j }u=3i+2j Round your answer to two decimal places.

Given vectors u=⟨−1,3⟩\mathbf { u } = \langle - 1,3 \rangleu=⟨−1,3⟩ and v=⟨1,4⟩\mathbf { v } = \langle 1,4 \ranglev=⟨1,4⟩ determine the quantity indicated below. −2u⋅−4v- 2 \mathbf { u }{ \cdot}- 4 \mathbf { v }−2u⋅−4v

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

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Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

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Properties of Logarithms

Exponential and Logarithmic Equations

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Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

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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

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Vectors in the Plane

Trigonometric Form of a Complex Number

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Linear Programming

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The Inverse of a Square Matrix

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Mathematical Induction

The Binomial Theorem

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Introduction to Conics Parabolas

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Parametric Equations

Polar Coordinates

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

Find the projection of u onto v if , $\mathbf { u } = \langle - 5 , - 4 \rangle$ , $\mathbf { v } = \langle 2 , - 5 \rangle$ .

Use vectors to find the measure of the angle at vertex B of triangle ABC,when $A = ( 5,1 )$ , $B = ( - 5,1 )$ ,and $C = ( - 3 , - 5 )$ .Round answer to two decimal places.

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

Use the dot product to find the magnitude of u if $\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }$

Determine whether u are v and orthogonal,parallel,or neither. $\mathbf { u } = \left\langle \frac { - 4 } { 3 } , \frac { 3 } { 2 } \right\rangle , \mathbf { v } = \langle 16 , - 18 \rangle$

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

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

Find the angle θ between the vectors. =\langle6,2\rangle =\langle7,0\rangle (Round the answer to 2 decimal places. )

Find the projection of u onto v. =\langle-5,-5\rangle =\langle-5,-1\rangle

Find the projection of u onto v. =\langle0,4\rangle =\langle3,20\rangle

Find the angle between the vectors u and v if $\mathbf { u } = 3 \mathbf { i } - 2 \mathbf { j }$ and $\mathbf { u } = 3 \mathbf { i } + 2 \mathbf { j }$ Round your answer to two decimal places.

Given vectors $\mathbf { u } = \langle - 1,3 \rangle$ and $\mathbf { v } = \langle 1,4 \rangle$ determine the quantity indicated below. $- 2 \mathbf { u }{ \cdot}- 4 \mathbf { v }$