wayground logo

Free Printable Worksheets

Font size

S
M
L
XL
Worksheets

Precalculus Application of Vectors

Total questions: 20

Worksheet time: 20mins

Name
Class
Date
1.
a)

a is the position vector of point A

b)

b is the direction vector of line L

c)

r is the position vector of all points in L, represented by P(x,y)

2.
a)

OB + BC = OC

b)

OA + AC = OC

c)

CB + B0 = -OC

d)

OD = 0.5(OA + AC)

3.

Vector a = 2i + 3j - 5k. What is the value of 3a?

a)

3i + 3j - 3k

b)

5i + 6j - 8k

c)

6i + 9j -15k

d)

6i + 6j - 15k

4.

Given parallel vectors u and v. Answer ALL that apply

a)

their scalar product is zero

b)

their scalar product is either 1 or -1

c)

u is a multiple of v

d)

magnitude of u equals the magnitude of v

5.

Find the component form of vector v.

a)

<6, 3><-6,\ 3>

b)

<6, 3><-6,\ -3>

c)

<6, 3><6,\ -3>

d)

<6, 3><6,\ 3>

6.

If g = <-1, 1>, y = <1, 1>, z = <-3, -3>, and v = <6, 8>, what is 4g + y + z - 5v?

a)

<24, 42>

b)

<-36, -38>

c)

<36, 38>

d)

<-30, -32>

7.

If a=4,2\vec{a} = \langle 4, -2 \rangle and b=1,2\vec{b} = \langle 1, 2 \rangle , what is the dot product ab\vec{a} \cdot \vec{b} ?

a)

0

b)

2

c)

6

d)

8

8.

Given an initial point A ( 2, 4 ) and terminal point B ( -8, 7 ), find the component form of the vector AB.

a)

〈-10,3〉

b)

〈-6,3〉

c)

〈10,11〉

d)

〈-6,-3〉

9.

Find the magnitude.

a)

4

b)

5

c)

3

d)

square root of 5

10.

The scalar product of u and v is zero, therefore...

a)

vectors u and v are parallel

b)

vectors u and v are perpendicular

c)

vectors u and v are equal

d)

vectors u and v are multiples

11.

A ferry departs from A(-25, 28). It takes 3 hours to reach its destination B(20, -32), travelling in as straight line with constant velocity. Distances are in km. Find the speed of the ferry.

a)

50 km/h

b)

55 km/h

c)

25 km/h

d)

20 km/h

12.

A ferry departs from A(-25, 28). It takes 3 hours to reach its destination B(20, -32), travelling in as straight line with constant velocity. Distances are in km. Find the velocity vector of the ferry.

a)

15i + 20j

b)

15i - 20j

c)

20i + 15j

d)

20i - 15j

13.

Vector is a quantity with:

a)

magnitude and direction

b)

magnitude

c)

direction

d)

none of the above

14.

Given the vector v = 3i -2j +6 k, the magnitude of a is:

a)

36

b)

49

c)

7

d)

6

15.

Given points A(2, 1) and B(-4, 1). Explain why the vector AB is parallel to the x-axis

a)

because vector AB is a multiple of the unit vector i

b)

because vector AB is a multiple of the unit vector j

c)

because vector AB is a multiple of the unit vector k

16.

A ferry departs from A(-25, 28). It takes 3 hours to reach its destination B(20, -32), travelling in as straight line with constant velocity. Distances are in km. Find the distance that the ferry travels.

a)

50 km

b)

55 km

c)

70 km

d)

75 km

17.

A vector is a mathematical structure that has both _______ and _______.

a)

direction, magnitude

b)

scope, sequence

c)

meat, potatoes

d)

scalar, vector

18.

Which are equivalent vectors?

a)

u and -u

b)

u and a

c)

u and v

d)

u and b

19.

Given an initial point R ( -12, 4 ) and terminal point S ( 28, -17 ), find the component form of the vector RS. Hint: get it into the pointy brackets.

a)

〈14,-13〉

b)

〈-14,13〉

c)

〈-40,-21〉

d)

〈40,-21〉

20.

Given u = <3, 7>, find 2u

a)

<21, 2>

b)

<6, 26>

c)

<6, 14>

d)

23