Find the angle θ between the vectors. $\begin{array} { l } \mathbf { u } = - 7 \mathbf { i } - 8 \mathbf { j } \\ \mathbf { v } = - 9 \mathbf { i } + 2 \mathbf { j } \end{array}$ (Round the answer to 2 decimal places. )

A) $71.34 ^ { \circ }$ B) $66.34 ^ { \circ }$ C) $61.34 ^ { \circ }$ D) $81.34 ^ { \circ }$ E) $76.34 ^ { \circ }$ A) $71.34 ^ { \circ }$ B) $66.34 ^ { \circ }$ C) $61.34 ^ { \circ }$ D) $81.34 ^ { \circ }$ E) $76.34 ^ { \circ }$

Exam 39:Vectors and Dot Products

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. $\langle \mathbf { u } \cdot \mathbf { v } \rangle - \langle \mathbf { u } \cdot \mathbf { w } \rangle$

(Multiple Choice)

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Question 41

Determine whether u are v and orthogonal,parallel,or neither. $\mathbf { u } = \langle - 4 , - 7 \rangle , \mathbf { v } = \langle 14,24 \rangle$

(Multiple Choice)

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Question 42

Use the dot product to find the magnitude of u. $\mathbf { u } = \langle 2 , - 9 \rangle$

(Multiple Choice)

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Question 43

Find the angle between the vectors u and v if $\mathbf { u } = \langle 3,4 \rangle$ ,and $\mathbf { v } = \langle - 1 , - 2 \rangle$ Round answer to two decimal places.

(Multiple Choice)

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Question 44

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

(Multiple Choice)

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Question 45

Use the vectors $\mathbf { u } = \langle 3,6 \rangle$ , $\mathbf { v } = \langle - 6,5 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar. $( \mathbf { u } \cdot \mathbf { v } ) \mathbf { v }$

(Multiple Choice)

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Question 46

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

(Multiple Choice)

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Question 47

Find the angle θ between the vectors. =-7-8 =-9+2 (Round the answer to 2 decimal places. )

(Multiple Choice)

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Question 48

Determine $u.v$ if $\| \mathbf { u } \| = 5$ , $\| \mathbf { v } \| = 4$ ,and $\theta = \frac { \pi } { 4 }$ where θ is the angle between u and v.Round answer to two decimal places.

(Multiple Choice)

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Question 49

A 475-pound trailer is sitting on an exit ramp inclined at 32° on Highway 35.How much force is required to keep the trailer from rolling back down the exit ramp? Round your answer to two decimal places.

(Multiple Choice)

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Question 50

The vector $\mathbf { u } = \langle 3800,5400 \rangle$ gives the number of units of two models of laptops produced by a company.The vector $\mathbf { v } = \langle 1350,1000 \rangle$ gives the prices (in dollars)of the two models of laptops,respectively.Identify the vector operation used to increase revenue by 3.5%.

(Multiple Choice)

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Question 51

Use the dot product to find the magnitude of u. $\mathbf { u } = 24 \mathbf { i } - 28 \mathbf { j }$

(Multiple Choice)

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Question 52

Given vectors $\mathbf { u } = \langle - 1 , - 2 \rangle$ and $\mathbf { v } = \langle 3,5 \rangle$ determine the quantity indicated below. $( 4 \mathbf { u } \cdot 2 \mathbf { v } ) \mathbf { u }$

(Multiple Choice)

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Question 53

Find the projection of u onto v if $\mathbf { u } = \langle 5 , - 3 \rangle$ , $\mathbf { v } = \langle - 1,4 \rangle$ .

(Multiple Choice)

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Question 54

A force of $y = 50$ pounds exerted at an angle of $30 ^ { \circ }$ above the horizontal is required to slide a table across a floor (see figure).The table is dragged $x = 12$ feet.Determine the work done in sliding the table. $A force of y = 50 pounds exerted at an angle of 30 ^ { \circ } above the horizontal is required to slide a table across a floor (see figure).The table is dragged x = 12 feet.Determine the work done in sliding the table. $

(Multiple Choice)

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Question 55

Determine whether u are v and orthogonal,parallel,or neither. $\mathbf { u } = \langle - 1,5 \rangle , \mathbf { v } = \langle - 10 , - 3 \rangle$

(Multiple Choice)

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Question 56

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

(Multiple Choice)

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Question 57

Use the dot product to find the magnitude of u if $\mathbf { u } = \langle 6 , - 2 \rangle$

(Multiple Choice)

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Question 58

Find the angle between the vectors u and v if $\mathbf { u } = \langle 3 , - 3 \rangle$ ,and $\mathbf { v } = \langle 1 , - 1 \rangle$ Round your answer to two decimal places.

(Multiple Choice)

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Question 59

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

(Multiple Choice)

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Question 60

Exam 39:Vectors and Dot Products

Determine whether u are v and orthogonal,parallel,or neither. u=⟨−4,−7⟩,v=⟨14,24⟩\mathbf { u } = \langle - 4 , - 7 \rangle , \mathbf { v } = \langle 14,24 \rangleu=⟨−4,−7⟩,v=⟨14,24⟩

Use the dot product to find the magnitude of u.​ u=⟨2,−9⟩\mathbf { u } = \langle 2 , - 9 \rangleu=⟨2,−9⟩ ​

Find the angle between the vectors u and v if u=⟨3,4⟩\mathbf { u } = \langle 3,4 \rangleu=⟨3,4⟩ ,and v=⟨−1,−2⟩\mathbf { v } = \langle - 1 , - 2 \ranglev=⟨−1,−2⟩ Round answer to two decimal places.

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

Use the vectors u=⟨3,6⟩\mathbf { u } = \langle 3,6 \rangleu=⟨3,6⟩ , v=⟨−6,5⟩\mathbf { v } = \langle - 6,5 \ranglev=⟨−6,5⟩ to find the indicated quantity.State whether the result is a vector or a scalar.​ (u⋅v)v( \mathbf { u } \cdot \mathbf { v } ) \mathbf { v }(u⋅v)v ​

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

Find the angle θ between the vectors. ​​ =-7-8 =-9+2 ​ (Round the answer to 2 decimal places. ) ​

Determine u.vu.vu.v if ∥u∥=5\| \mathbf { u } \| = 5∥u∥=5 , ∥v∥=4\| \mathbf { v } \| = 4∥v∥=4 ,and θ=π4\theta = \frac { \pi } { 4 }θ=4π​ where θ is the angle between u and v.Round answer to two decimal places.

A 475-pound trailer is sitting on an exit ramp inclined at 32° on Highway 35.How much force is required to keep the trailer from rolling back down the exit ramp? Round your answer to two decimal places.

Use the dot product to find the magnitude of u.​ u=24i−28j\mathbf { u } = 24 \mathbf { i } - 28 \mathbf { j }u=24i−28j ​

Given vectors u=⟨−1,−2⟩\mathbf { u } = \langle - 1 , - 2 \rangleu=⟨−1,−2⟩ and v=⟨3,5⟩\mathbf { v } = \langle 3,5 \ranglev=⟨3,5⟩ determine the quantity indicated below. (4u⋅2v)u( 4 \mathbf { u } \cdot 2 \mathbf { v } ) \mathbf { u }(4u⋅2v)u

Find the projection of u onto v if u=⟨5,−3⟩\mathbf { u } = \langle 5 , - 3 \rangleu=⟨5,−3⟩ , v=⟨−1,4⟩\mathbf { v } = \langle - 1,4 \ranglev=⟨−1,4⟩ . ​

A force of y=50y = 50y=50 pounds exerted at an angle of 30∘30 ^ { \circ }30∘ above the horizontal is required to slide a table across a floor (see figure).The table is dragged x=12x = 12x=12 feet.Determine the work done in sliding the table.​ ​

Determine whether u are v and orthogonal,parallel,or neither. u=⟨−1,5⟩,v=⟨−10,−3⟩\mathbf { u } = \langle - 1,5 \rangle , \mathbf { v } = \langle - 10 , - 3 \rangleu=⟨−1,5⟩,v=⟨−10,−3⟩

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

Use the dot product to find the magnitude of u if u=⟨6,−2⟩\mathbf { u } = \langle 6 , - 2 \rangleu=⟨6,−2⟩

Find the angle between the vectors u and v if u=⟨3,−3⟩\mathbf { u } = \langle 3 , - 3 \rangleu=⟨3,−3⟩ ,and v=⟨1,−1⟩\mathbf { v } = \langle 1 , - 1 \ranglev=⟨1,−1⟩ Round your answer to two decimal places.

Use the vectors u=⟨2,2⟩\mathbf { u } = \langle 2,2 \rangleu=⟨2,2⟩ , v=⟨−2,2⟩\mathbf { v } = \langle - 2,2 \ranglev=⟨−2,2⟩ to find the indicated quantity.State whether the result is a vector or a scalar.​ 3u⋅v3 \mathbf { u } \cdot \mathbf { v }3u⋅v ​

Rectangular Coordinates

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Determine whether u are v and orthogonal,parallel,or neither. $\mathbf { u } = \langle - 4 , - 7 \rangle , \mathbf { v } = \langle 14,24 \rangle$

Use the dot product to find the magnitude of u. $\mathbf { u } = \langle 2 , - 9 \rangle$

Find the angle between the vectors u and v if $\mathbf { u } = \langle 3,4 \rangle$ ,and $\mathbf { v } = \langle - 1 , - 2 \rangle$ Round answer to two decimal places.

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

Use the vectors $\mathbf { u } = \langle 3,6 \rangle$ , $\mathbf { v } = \langle - 6,5 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar. $( \mathbf { u } \cdot \mathbf { v } ) \mathbf { v }$

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

Find the angle θ between the vectors. =-7-8 =-9+2 (Round the answer to 2 decimal places. )

Determine $u.v$ if $\| \mathbf { u } \| = 5$ , $\| \mathbf { v } \| = 4$ ,and $\theta = \frac { \pi } { 4 }$ where θ is the angle between u and v.Round answer to two decimal places.

Use the dot product to find the magnitude of u. $\mathbf { u } = 24 \mathbf { i } - 28 \mathbf { j }$

Given vectors $\mathbf { u } = \langle - 1 , - 2 \rangle$ and $\mathbf { v } = \langle 3,5 \rangle$ determine the quantity indicated below. $( 4 \mathbf { u } \cdot 2 \mathbf { v } ) \mathbf { u }$

Find the projection of u onto v if $\mathbf { u } = \langle 5 , - 3 \rangle$ , $\mathbf { v } = \langle - 1,4 \rangle$ .

Determine whether u are v and orthogonal,parallel,or neither. $\mathbf { u } = \langle - 1,5 \rangle , \mathbf { v } = \langle - 10 , - 3 \rangle$

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

Use the dot product to find the magnitude of u if $\mathbf { u } = \langle 6 , - 2 \rangle$

Find the angle between the vectors u and v if $\mathbf { u } = \langle 3 , - 3 \rangle$ ,and $\mathbf { v } = \langle 1 , - 1 \rangle$ Round your answer to two decimal places.

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