Question 1

Let u be the vector with initial point $P ( 7 , - 3 )$ and terminal point $Q ( 1,4 )$
) Express u in terms of i and j

Accepted Answer

A)  $\mathbf { u } = - 6 \mathbf { i } + 6 \mathbf { j }$ 
B)  $\mathbf { u } = - 6 \mathbf { i } + 7 \mathbf { j }$ 
C)  $\mathbf { u } = - 3 \mathbf { i } - 2 \mathbf { j }$ 
D)  $\mathbf { u } = - 6 \mathbf { i } + \mathbf { j }$ 
E) none 
A)  $\mathbf { u } = - 6 \mathbf { i } + 6 \mathbf { j }$ 
B)  $\mathbf { u } = - 6 \mathbf { i } + 7 \mathbf { j }$ 
C)  $\mathbf { u } = - 3 \mathbf { i } - 2 \mathbf { j }$ 
D)  $\mathbf { u } = - 6 \mathbf { i } + \mathbf { j }$ 
E) none

Question 2

If the vector v has initial point P, what is its terminal point? $\mathbf { v } = ( 0,0,1 ) , P ( 1,1 , - 1 )$

Accepted Answer

A)  $( 2,1,0 )$ 
B)  $( 1,1,0 )$ 
C)  $( - 1,1,0 )$ 
D)  $( 1 , - 1,0 )$ 
E)  none of these 
A)  $( 2,1,0 )$ 
B)  $( 1,1,0 )$ 
C)  $( - 1,1,0 )$ 
D)  $( 1 , - 1,0 )$ 
E)  none of these

Question 3

Find the direction of the vector $\mathbf { v } = 120 \mathbf { i } - 120 \sqrt { 3 } \mathbf { j }$ 
.

Accepted Answer

The answer of Find the direction of the vector \(\mathbf...

Question 4

A jet heads in the direction N $30 ^ { \circ }$ 
E at a speed of $400$ 
mi/h. If the jet experiences a $20$ 
mi/h crosswind flowing due east, find (a) the true velocity $\boldsymbol { Y r } ^ { \mathrm { r } }$ 
of the jet
b) the true speed of the jet
c) the direction of the jet.

Accepted Answer

The answer of A jet heads in the direction N...

Question 5

Find $| \mathrm { v } |$ and $| \mathbf { u } + \mathbf { y } |$, given that $\mathbf { u } = - \mathbf { j }$ and $\mathbf { v } = \mathbf { i }$

Accepted Answer

A)  $| \mathrm { v } | = 1$
, $| \mathbf { u } + \mathbf { v } | = \sqrt { 2 }$ 
B)  $| v | = - 1$
, $| \mathbf { u } + \mathbf { v } | = - \sqrt { 2 }$ 
C)  $| \mathrm { v } | = \sqrt { 2 }$
, $| \mathbf { u } + \mathbf { y } | = 1$ 
D)  $| \mathrm { v } | = \sqrt { 2 }$
, $| \mathbf { u } + \mathbf { v } | = \sqrt { 2 }$ 
E) none 
A)  $| \mathrm { v } | = 1$
, $| \mathbf { u } + \mathbf { v } | = \sqrt { 2 }$ 
B)  $| v | = - 1$
, $| \mathbf { u } + \mathbf { v } | = - \sqrt { 2 }$ 
C)  $| \mathrm { v } | = \sqrt { 2 }$
, $| \mathbf { u } + \mathbf { y } | = 1$ 
D)  $| \mathrm { v } | = \sqrt { 2 }$
, $| \mathbf { u } + \mathbf { v } | = \sqrt { 2 }$ 
E) none

Question 6

Find the angle between $u$ and $\mathbf { Y }$.
 $\mathbf { u } = \langle - 3,2 ) , \mathbf { v } = \langle 6 , - 2 \rangle$

Accepted Answer

A)  $146.5 ^ { \circ }$ 
B)  $51.5 ^ { \circ }$ 
C)  $33.70 ^ { \circ }$ 
D)  $18.41 ^ { \circ }$ 
E)  $164.74 ^ { \circ }$ 
A)  $146.5 ^ { \circ }$ 
B)  $51.5 ^ { \circ }$ 
C)  $33.70 ^ { \circ }$ 
D)  $18.41 ^ { \circ }$ 
E)  $164.74 ^ { \circ }$

Question 7

Let u be the vector with initial point $P ( 7,3 )$ and terminal point $Q ( 1,4 )$
) Express u in terms of i and j

Accepted Answer

A)  $\mathbf { u } = - 6 \mathbf { i } + 6 \mathbf { j }$ 
B)  $\mathbf { u } = - 6 \mathbf { i } + 7 \mathbf { j }$ 
C)  $\mathbf { u } = - 3 \mathbf { i } - 2 \mathbf { j }$ 
D)  $\mathbf { u } = - 6 \mathbf { i } + \mathbf { j }$ 
E)  $\mathbf { u } = - 6 \mathbf { i } - 2 \mathbf { j }$ 
A)  $\mathbf { u } = - 6 \mathbf { i } + 6 \mathbf { j }$ 
B)  $\mathbf { u } = - 6 \mathbf { i } + 7 \mathbf { j }$ 
C)  $\mathbf { u } = - 3 \mathbf { i } - 2 \mathbf { j }$ 
D)  $\mathbf { u } = - 6 \mathbf { i } + \mathbf { j }$ 
E)  $\mathbf { u } = - 6 \mathbf { i } - 2 \mathbf { j }$

Question 8

Find $| \mathrm { v } |$ 
and $| \mathbf { u } + \mathbf { y } |$ 
, given that $\mathbf { u } = 2 \mathbf { i } - \mathbf { j }$ 
and $\mathbf { v } = \mathbf { i }$ 
.

Accepted Answer

The answer of Find $| \mathrm { v } |$...

Question 9

Find the magnitude and direction (in degrees) of the vector $\mathbf { v } = - \mathbf { i } - \sqrt { 5 } \mathbf { j }$ 
.

Accepted Answer

@#LAT-DLM& 
, direct

Question 10

Find the vector $\mathbf { Y }$ having length $| \mathrm { v } | = 4$
, and direction $\theta = 225 ^ { \circ }$

Accepted Answer

A)  $\mathrm { v } = \langle - 1,1 \rangle$ 
B)  $\mathrm { v } = \langle - 2 \sqrt { 2 } , - 2 \sqrt { 2 } \rangle$ 
C)  $\mathrm { v } = \langle - \sqrt { 2 } , \sqrt { 2 } \rangle$ 
D)  $\mathbf {v } = \langle 1,1 \rangle$ 
E)  $\mathrm { v } = \langle - 2,2 \rangle$ 
A)  $\mathrm { v } = \langle - 1,1 \rangle$ 
B)  $\mathrm { v } = \langle - 2 \sqrt { 2 } , - 2 \sqrt { 2 } \rangle$ 
C)  $\mathrm { v } = \langle - \sqrt { 2 } , \sqrt { 2 } \rangle$ 
D)  $\mathbf {v } = \langle 1,1 \rangle$ 
E)  $\mathrm { v } = \langle - 2,2 \rangle$

Question 11

Determine whether $\mathbf { u }= \left( - \frac { 1 } { 2 } , 2 \right\rangle$ 
is orthogonal to $\boldsymbol { v } = \left( - 2 , \frac { 1 } { 2 } \right)$ 
. Justify your answer.

Accepted Answer

The answer of Determine whether \(\mathbf { u }= \left(...

Question 12

Find the center and radius of the sphere. $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 4 x + 4 - 8 y = 0$

Accepted Answer

A)  $C ( 2,2,4 ) ; r = \sqrt { 2 }$ 
B)  $C ( 0,2,4 ) ; r = 4$ 
C)  $C ( 2,4,0 ) ; r = \sqrt { 2 }$ 
D)  $C ( 2,4,0 ) ; r = 2$ 
E) none of these 
A)  $C ( 2,2,4 ) ; r = \sqrt { 2 }$ 
B)  $C ( 0,2,4 ) ; r = 4$ 
C)  $C ( 2,4,0 ) ; r = \sqrt { 2 }$ 
D)  $C ( 2,4,0 ) ; r = 2$ 
E) none of these

Question 13

A water tank is in the shape of a sphere of radius 15 feet. The tank is supported on a metal circle 12 feet below the center of the sphere, as shown in the figure. Find the radius of the metal circle.

Accepted Answer

The answer of A water tank is in the shape...

Question 14

Two vectors u and v are given. Find the angle (expressed in degrees) between u and v. $\mathbf { u } = \langle 4,0 , - 2 \rangle , \mathbf { v } = \langle 2,1,0 \rangle$

Accepted Answer

A)  $1.3 ^ { \circ }$ 
B)  $1.2 ^ { \circ }$ 
C)  $63.9 ^ { \circ }$ 
D)  $36.9 ^ { \circ }$ 
E)  none of these 
A)  $1.3 ^ { \circ }$ 
B)  $1.2 ^ { \circ }$ 
C)  $63.9 ^ { \circ }$ 
D)  $36.9 ^ { \circ }$ 
E)  none of these

Question 15

Find the angle between $u$ and $\mathbf { Y }$
) $\mathbf { u } = \langle - 3,2 ) , \mathbf { v } = \langle 6 , - 2 \rangle$

Accepted Answer

A)  $146.5 ^ { \circ }$ 
B)  $51.5 ^ { \circ }$ 
C)  $33.70 ^ { \circ }$ 
D)  $18.41 ^ { \circ }$ 
E)  $164.74 ^ { \circ }$ 
A)  $146.5 ^ { \circ }$ 
B)  $51.5 ^ { \circ }$ 
C)  $33.70 ^ { \circ }$ 
D)  $18.41 ^ { \circ }$ 
E)  $164.74 ^ { \circ }$

Question 16

Find $\mathbf { u } \cdot \mathbf { Y }$ . 
$\mathbf { u } = ( 5,0 ) , \mathbf { v } = ( \sqrt { 3 } , 1 )$

Accepted Answer

The answer of Find \(\mathbf { u } \cdot \mathbf...

Question 17

Two vectors a and b are given. (a) Find a vector perpendicular to both a and
b
b)Find a unit vector perpendicular to both a and
b. $\mathbf { a } = 3 \mathbf { j } - 5 \mathbf { k } , \mathbf { b } = \mathbf { i } + 2 \mathbf { k }$

Accepted Answer

The answer of Two vectors a and b are given....

Let u be the vector with initial point $P ( 7 , - 3 )$ and terminal point $Q ( 1,4 )$ ) Express u in terms of i and j

If the vector v has initial point P, what is its terminal point? $\mathbf { v } = ( 0,0,1 ) , P ( 1,1 , - 1 )$

Find the direction of the vector $\mathbf { v } = 120 \mathbf { i } - 120 \sqrt { 3 } \mathbf { j }$ .

A jet heads in the direction N $30 ^ { \circ }$ E at a speed of $400$ mi/h. If the jet experiences a $20$ mi/h crosswind flowing due east, find (a) the true velocity $\boldsymbol { Y r } ^ { \mathrm { r } }$ of the jet b) the true speed of the jet c) the direction of the jet.

Find $| \mathrm { v } |$ and $| \mathbf { u } + \mathbf { y } |$ , given that $\mathbf { u } = - \mathbf { j }$ and $\mathbf { v } = \mathbf { i }$

Find the angle between $u$ and $\mathbf { Y }$ . $\mathbf { u } = \langle - 3,2 ) , \mathbf { v } = \langle 6 , - 2 \rangle$

Let u be the vector with initial point $P ( 7,3 )$ and terminal point $Q ( 1,4 )$ ) Express u in terms of i and j

Find $| \mathrm { v } |$ and $| \mathbf { u } + \mathbf { y } |$ , given that $\mathbf { u } = 2 \mathbf { i } - \mathbf { j }$ and $\mathbf { v } = \mathbf { i }$ .

Find the magnitude and direction (in degrees) of the vector $\mathbf { v } = - \mathbf { i } - \sqrt { 5 } \mathbf { j }$ .

Find the vector $\mathbf { Y }$ having length $| \mathrm { v } | = 4$ , and direction $\theta = 225 ^ { \circ }$

Determine whether $\mathbf { u }= \left( - \frac { 1 } { 2 } , 2 \right\rangle$ is orthogonal to $\boldsymbol { v } = \left( - 2 , \frac { 1 } { 2 } \right)$ . Justify your answer.

Find the center and radius of the sphere. $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 4 x + 4 - 8 y = 0$

A water tank is in the shape of a sphere of radius 15 feet. The tank is supported on a metal circle 12 feet below the center of the sphere, as shown in the figure. Find the radius of the metal circle.

Two vectors u and v are given. Find the angle (expressed in degrees) between u and v. $\mathbf { u } = \langle 4,0 , - 2 \rangle , \mathbf { v } = \langle 2,1,0 \rangle$

Find the angle between $u$ and $\mathbf { Y }$ ) $\mathbf { u } = \langle - 3,2 ) , \mathbf { v } = \langle 6 , - 2 \rangle$

Find $\mathbf { u } \cdot \mathbf { Y }$ . $\mathbf { u } = ( 5,0 ) , \mathbf { v } = ( \sqrt { 3 } , 1 )$

Two vectors a and b are given. (a) Find a vector perpendicular to both a and b b)Find a unit vector perpendicular to both a and b. $\mathbf { a } = 3 \mathbf { j } - 5 \mathbf { k } , \mathbf { b } = \mathbf { i } + 2 \mathbf { k }$

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Exam 10: Systems of Equations and Inequalities

Let u be the vector with initial point P(7,−3)P ( 7 , - 3 )P(7,−3) and terminal point Q(1,4)Q ( 1,4 )Q(1,4) ) Express u in terms of i and j

If the vector v has initial point P, what is its terminal point? v=(0,0,1),P(1,1,−1)\mathbf { v } = ( 0,0,1 ) , P ( 1,1 , - 1 )v=(0,0,1),P(1,1,−1)

Find the direction of the vector v=120i−1203j\mathbf { v } = 120 \mathbf { i } - 120 \sqrt { 3 } \mathbf { j }v=120i−1203​j .

A jet heads in the direction N 30∘30 ^ { \circ }30∘ E at a speed of 400400400 mi/h. If the jet experiences a 202020 mi/h crosswind flowing due east, find (a) the true velocity Yrr\boldsymbol { Y r } ^ { \mathrm { r } }Yrr of the jet b) the true speed of the jet c) the direction of the jet.

Find ∣v∣| \mathrm { v } |∣v∣ and ∣u+y∣| \mathbf { u } + \mathbf { y } |∣u+y∣ , given that u=−j\mathbf { u } = - \mathbf { j }u=−j and v=i\mathbf { v } = \mathbf { i }v=i

Find the angle between uuu and Y\mathbf { Y }Y . u=⟨−3,2),v=⟨6,−2⟩\mathbf { u } = \langle - 3,2 ) , \mathbf { v } = \langle 6 , - 2 \rangleu=⟨−3,2),v=⟨6,−2⟩

Let u be the vector with initial point P(7,3)P ( 7,3 )P(7,3) and terminal point Q(1,4)Q ( 1,4 )Q(1,4) ) Express u in terms of i and j

Find ∣v∣| \mathrm { v } |∣v∣ and ∣u+y∣| \mathbf { u } + \mathbf { y } |∣u+y∣ , given that u=2i−j\mathbf { u } = 2 \mathbf { i } - \mathbf { j }u=2i−j and v=i\mathbf { v } = \mathbf { i }v=i .

Find the magnitude and direction (in degrees) of the vector v=−i−5j\mathbf { v } = - \mathbf { i } - \sqrt { 5 } \mathbf { j }v=−i−5​j .

Find the vector Y\mathbf { Y }Y having length ∣v∣=4| \mathrm { v } | = 4∣v∣=4 , and direction θ=225∘\theta = 225 ^ { \circ }θ=225∘

Determine whether u=(−12,2⟩\mathbf { u }= \left( - \frac { 1 } { 2 } , 2 \right\rangleu=(−21​,2⟩ is orthogonal to v=(−2,12)\boldsymbol { v } = \left( - 2 , \frac { 1 } { 2 } \right)v=(−2,21​) . Justify your answer.

Find the center and radius of the sphere. x2+y2+z2−4x+4−8y=0x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 4 x + 4 - 8 y = 0x2+y2+z2−4x+4−8y=0

A water tank is in the shape of a sphere of radius 15 feet. The tank is supported on a metal circle 12 feet below the center of the sphere, as shown in the figure. Find the radius of the metal circle.

Two vectors u and v are given. Find the angle (expressed in degrees) between u and v. u=⟨4,0,−2⟩,v=⟨2,1,0⟩\mathbf { u } = \langle 4,0 , - 2 \rangle , \mathbf { v } = \langle 2,1,0 \rangleu=⟨4,0,−2⟩,v=⟨2,1,0⟩

Find the angle between uuu and Y\mathbf { Y }Y ) u=⟨−3,2),v=⟨6,−2⟩\mathbf { u } = \langle - 3,2 ) , \mathbf { v } = \langle 6 , - 2 \rangleu=⟨−3,2),v=⟨6,−2⟩

Find u⋅Y\mathbf { u } \cdot \mathbf { Y }u⋅Y . u=(5,0),v=(3,1)\mathbf { u } = ( 5,0 ) , \mathbf { v } = ( \sqrt { 3 } , 1 )u=(5,0),v=(3​,1)

Two vectors a and b are given. (a) Find a vector perpendicular to both a and b b)Find a unit vector perpendicular to both a and b. a=3j−5k,b=i+2k\mathbf { a } = 3 \mathbf { j } - 5 \mathbf { k } , \mathbf { b } = \mathbf { i } + 2 \mathbf { k }a=3j−5k,b=i+2k

Equations and Graphs

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Polynomial and Rational Functions

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Matrices and Determinants

Conic Sections

Sequences and Series

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Filters

Let u be the vector with initial point $P ( 7 , - 3 )$ and terminal point $Q ( 1,4 )$ ) Express u in terms of i and j

If the vector v has initial point P, what is its terminal point? $\mathbf { v } = ( 0,0,1 ) , P ( 1,1 , - 1 )$

Find the direction of the vector $\mathbf { v } = 120 \mathbf { i } - 120 \sqrt { 3 } \mathbf { j }$ .

A jet heads in the direction N $30 ^ { \circ }$ E at a speed of $400$ mi/h. If the jet experiences a $20$ mi/h crosswind flowing due east, find (a) the true velocity $\boldsymbol { Y r } ^ { \mathrm { r } }$ of the jet b) the true speed of the jet c) the direction of the jet.

Find $| \mathrm { v } |$ and $| \mathbf { u } + \mathbf { y } |$ , given that $\mathbf { u } = - \mathbf { j }$ and $\mathbf { v } = \mathbf { i }$

Find the angle between $u$ and $\mathbf { Y }$ . $\mathbf { u } = \langle - 3,2 ) , \mathbf { v } = \langle 6 , - 2 \rangle$

Let u be the vector with initial point $P ( 7,3 )$ and terminal point $Q ( 1,4 )$ ) Express u in terms of i and j

Find $| \mathrm { v } |$ and $| \mathbf { u } + \mathbf { y } |$ , given that $\mathbf { u } = 2 \mathbf { i } - \mathbf { j }$ and $\mathbf { v } = \mathbf { i }$ .

Find the magnitude and direction (in degrees) of the vector $\mathbf { v } = - \mathbf { i } - \sqrt { 5 } \mathbf { j }$ .

Find the vector $\mathbf { Y }$ having length $| \mathrm { v } | = 4$ , and direction $\theta = 225 ^ { \circ }$

Determine whether $\mathbf { u }= \left( - \frac { 1 } { 2 } , 2 \right\rangle$ is orthogonal to $\boldsymbol { v } = \left( - 2 , \frac { 1 } { 2 } \right)$ . Justify your answer.

Find the center and radius of the sphere. $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 4 x + 4 - 8 y = 0$

Two vectors u and v are given. Find the angle (expressed in degrees) between u and v. $\mathbf { u } = \langle 4,0 , - 2 \rangle , \mathbf { v } = \langle 2,1,0 \rangle$

Find the angle between $u$ and $\mathbf { Y }$ ) $\mathbf { u } = \langle - 3,2 ) , \mathbf { v } = \langle 6 , - 2 \rangle$

Find $\mathbf { u } \cdot \mathbf { Y }$ . $\mathbf { u } = ( 5,0 ) , \mathbf { v } = ( \sqrt { 3 } , 1 )$

Two vectors a and b are given. (a) Find a vector perpendicular to both a and b b)Find a unit vector perpendicular to both a and b. $\mathbf { a } = 3 \mathbf { j } - 5 \mathbf { k } , \mathbf { b } = \mathbf { i } + 2 \mathbf { k }$