Quiz about 5-3 Vectors and Dot Product (AP Precalculus)

Question 1

What is the magnitude of the vector $$\overrightarrow{v}=$$ ?

Accepted Answer

All of these are correct.

Answer

$$\left|\left|\overrightarrow{v}\right|\right|=\sqrt{x^2+y^2+z^2}$$

Answer

$$\left|\left|\overrightarrow{v}\right|\right|=\sqrt[]{\overrightarrow{v}\cdot\overrightarrow{v}}$$

Answer

Magnitude is the length of $$\overrightarrow{v}$$ tip-to-tail

Question 2

What is the xy-component form of the two-dimensional vector that has magnitude 52 in direction 218 degrees?

Accepted Answer

<-41,-32>

Answer

<-17,-49>

Answer

<-32,-41>

Answer

<-49,-17>

Question 3

What is the angle of the vector $$\overrightarrow{v}=<106,-238>$$ ?

Accepted Answer

294

Answer

314

Answer

246

Answer

336

Question 4

What is the magnitude of the vector A = < 65, -26 > ?

Accepted Answer

70

Answer

60

Answer

91

Answer

166

Question 5

Calculate the magnitude of the vector: $$\overrightarrow{u}=<-45,28>$$ .

Accepted Answer

53

Answer

35

Answer

48

Answer

17

Question 6

What is the magnitude of the 3-dimensional vector <-12,-16,-15> ?

Accepted Answer

25

Answer

19

Answer

34

Answer

43

Question 7

What is the distance between point P=(3, 1, -8) and Q=(-12, 7, -18) ?

To find distance between two points, calculate the magnitude of the vector from P to Q.

Accepted Answer

19

Answer

11

Answer

31

Answer

115

Question 8

Calculate the dot product u.v of vector v = <3,5> with vector w=<8,1>.

Accepted Answer

29

Answer

23

Answer

6

Answer

14

Question 9

Suppose that a = <-21, 9, -5> and b = <-7, 12, 2>. What is the value of their dot product: a.b?

Accepted Answer

245

Answer

56

Answer

-49

Answer

157

Question 10

The vector $$\overrightarrow{v}=\ <-4,6>$$ is perpendicular to the vector $$\overrightarrow{w}\ =\ <3,y>$$ . What is the value of $$y$$ ?

Accepted Answer

2

Answer

1

Answer

-8

Answer

-4

Question 11

What is the magnitude of $$\overrightarrow{v}=<-3,8,3>$$ ?

Accepted Answer

9

Answer

8

Answer

82

Answer

6

Question 12

Fill in the blank: Calculate the missing component of the given vector operation. Suppose $$\overrightarrow{u}=<3,-9>,\ \overrightarrow{v}=<4,-2>.\ $$ Then $$5\overrightarrow{v}-\overrightarrow{u}=$$ .

Accepted Answer

17

Answer

11

Answer

24

Answer

5

Question 13

Fill in the blank: Calculate the missing component of the given vector operation.

Suppose $$\overrightarrow{a}=<-21,9,-5>,\ \overrightarrow{b}=<-7,12,2>.\ $$ Then $$2\overrightarrow{a}-3\overrightarrow{b}=<-21,\ ??\ ,-16>.\ $$

Accepted Answer

-18

Answer

36

Answer

-3

Answer

6

Question 14

What is the dot product of vector p=<3, 1, -8> and q=<-12, 7, -18> ? (Calculate p.q)

Accepted Answer

115

Answer

-173

Answer

19

Answer

31

Question 15

Suppose $$\overrightarrow{a}=<1,4,-3>,\ \overrightarrow{b}=<2,-1,5>.\ $$ Calculate the dot product of the vector $$\overrightarrow{\left(a+b\right)}$$ with the vector $$\overrightarrow{\left(a-b\right)}$$ .

Accepted Answer

-4

Answer

-17

Answer

56

Answer

34

Question 16

What is the unit vector in the same direction as < 7, -24 > ?

Accepted Answer

< 0.28, -0.96 >

Answer

< 0.14, -0.86 >

Answer

< 7/31, -24/31 >

Answer

< 0.35, -0.93 >

Question 17

Which of the following is the unit vector in the same direction as < -9, -12 > ?

Accepted Answer

< -3/5, -4/5 >

Answer

< 3/5, 4/5 >

Answer

< 3/5, -4/5 >

Answer

< -3/5, 4/5 >

Question 18

Which of the following is the unit vector in the same direction as < 1, -2, 2 > ?

Accepted Answer

< 1/3, -2/3, 2/3 >

Answer

< 1/4, -1/2, 1/2 >

Answer

< 1/5, -2/5, 2/5 >

Answer

< 1/9, -2/9, 2/9 >

5-3 Vectors and Dot Product (AP Precalculus)

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