Question 1

Given $\mathbf { u } = - 3 \mathbf { i } + 2 \mathbf { j }$ and $\mathbf { u } = 4 \mathbf { i } - \mathbf { j }$ ,find $u\cdot v$ .

Accepted Answer

A) -10 
B) -14 
C) 11 
D) -5 
E) -12 
A) -10 
B) -14 
C) 11 
D) -5 
E) -12

Question 2

Find the dot product of u and v.​ $$\begin{array} { l } 
\mathbf { u } = 6 \mathbf { i } - 4 \mathbf { j } \
\mathbf { v } = \mathbf { i } - \mathbf { j }
\end{array}$$ ​

Accepted Answer

A) 14 
B) 6 
C) 12 
D) 10 
E) 8 
A) 14 
B) 6 
C) 12 
D) 10 
E) 8

Question 3

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 4

Find the angle θ between the vectors. ​​ $\begin{array} { l } 
\mathbf { u } = 6 \mathbf { i } - 1 \mathbf { j } \
\mathbf { v } = 7 \mathbf { i } + 2 \mathbf { j }
\end{array}$ ​
(Round the answer to 2 decimal places. )
​

Accepted Answer

A)  $25.41 ^ { \circ }$ 
B)  $45.41 ^ { \circ }$ 
C)  $30.41 ^ { \circ }$ 
D)  $35.41 ^ { \circ }$ 
E)  $40.41 ^ { \circ }$ 
A)  $25.41 ^ { \circ }$ 
B)  $45.41 ^ { \circ }$ 
C)  $30.41 ^ { \circ }$ 
D)  $35.41 ^ { \circ }$ 
E)  $40.41 ^ { \circ }$

Question 5

Find the dot product of u and v.​ $$\begin{array} { l } 
\mathbf { u } = \langle - 7,1 \rangle \
\mathbf { v } = \langle 4 , - 5 \rangle
\end{array}$$ ​

Accepted Answer

A) -31 
B) -29 
C) -33 
D) -37 
E) -35 
A) -31 
B) -29 
C) -33 
D) -37 
E) -35

Question 6

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 7

A tractor pulls a log 900 meters,and the tension in the cable connecting the tractor and log is approximately 16,691 newtons.The direction of the force is $35 ^ { \circ }$ above the horizontal.Approximate the work done in pulling the log. ​
(Round the answer to two decimal places. )
​

Accepted Answer

A) 12,305,260.09 N-m 
B) 12,305,220.09 N-m 
C) 12,305,300.09 N-m 
D) 12,305,280.090 N-m 
E) 12,305,240.09 N-m 
A) 12,305,260.09 N-m 
B) 12,305,220.09 N-m 
C) 12,305,300.09 N-m 
D) 12,305,280.090 N-m 
E) 12,305,240.09 N-m

Exam 39:Vectors and Dot Products

Given u=−3i+2j\mathbf { u } = - 3 \mathbf { i } + 2 \mathbf { j }u=−3i+2j and u=4i−j\mathbf { u } = 4 \mathbf { i } - \mathbf { j }u=4i−j ,find u⋅vu\cdot vu⋅v .

Find the dot product of u and v.​ =6-4 =- ​

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

Find the angle θ between the vectors. ​​ =6-1 =7+2 ​ (Round the answer to 2 decimal places. ) ​

Find the dot product of u and v.​ =\langle-7,1\rangle =\langle4,-5\rangle ​

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.

A tractor pulls a log 900 meters,and the tension in the cable connecting the tractor and log is approximately 16,691 newtons.The direction of the force is 35∘35 ^ { \circ }35∘ above the horizontal.Approximate the work done in pulling the log. ​ (Round the answer to two decimal places. ) ​

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Given $\mathbf { u } = - 3 \mathbf { i } + 2 \mathbf { j }$ and $\mathbf { u } = 4 \mathbf { i } - \mathbf { j }$ ,find $u\cdot v$ .

Find the dot product of u and v. =6-4 =-

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

Find the angle θ between the vectors. =6-1 =7+2 (Round the answer to 2 decimal places. )

Find the dot product of u and v. =\langle-7,1\rangle =\langle4,-5\rangle

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.

A tractor pulls a log 900 meters,and the tension in the cable connecting the tractor and log is approximately 16,691 newtons.The direction of the force is $35 ^ { \circ }$ above the horizontal.Approximate the work done in pulling the log. (Round the answer to two decimal places. )