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Precalculus

Vector Operations Notes

Name___________________________________

Date________________ Period____

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-1-

Find the component form of the resultant vector.

1) u = -4, 11Find the vector opposite u

2) Given: A = (3, 4) B = (-3, 6)Find the vector opposite AB

Express the resultant vector as a linear combination of unit vectors i and j.

3) f = 8, 240°Find the vector opposite f

4) f = 6i - 4jFind: -2f

5) Given: P = (-2, -7) Q = (-4, -5)Find: 2PQ

Find the component form of the resultant vector.

6) a = 0, 2g = -12, 10Find: a - g

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-2-

7) Given: T = (2, -8) X = (1, 4) Y = (-2, 1) Z = (10, 6)Find: TX + YZ

8) Given: T = (-8, -3) X = (-9, -6) Y = (4, 7) Z = (9, 9)Find: 2TX + 4YZ

Express the resultant vector as a linear combination of unit vectors i and j.

9) f = 7i - 4jv = 5i - 8jFind: 6f - 7v

Draw a diagram to illustrate the horizontal and vertical components of the vector. Then findthe value of each component.

10) m = 22, 289°

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-3-

Draw a vector diagram to find the resultant of each pair of vectors using the triangle method. Then state the magnitude and direction angle of the resultant.

11) m = 11, 3 n = 9, -12 12) a = -3, 4 b = 3, 13

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-4-

13) m = -20, -1 n = 8, 15 14) t = -15, 5 u = 4, -10

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Worksheet by Kuta Software LLC

Precalculus

Vector Operations Notes

Name___________________________________

Date________________ Period____

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-1-

Find the component form of the resultant vector.

1) u = -4, 11Find the vector opposite u

4, - 11

2) Given: A = (3, 4) B = (-3, 6)Find the vector opposite AB

6, -2

Express the resultant vector as a linear combination of unit vectors i and j.

3) f = 8, 240°Find the vector opposite f

4i + 6.93j

4) f = 6i - 4jFind: -2f

-12i + 8j

5) Given: P = (-2, -7) Q = (-4, -5)Find: 2PQ

-4i + 4j

Find the component form of the resultant vector.

6) a = 0, 2g = -12, 10Find: a - g

12, -8

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-2-

7) Given: T = (2, -8) X = (1, 4) Y = (-2, 1) Z = (10, 6)Find: TX + YZ

11, 17

8) Given: T = (-8, -3) X = (-9, -6) Y = (4, 7) Z = (9, 9)Find: 2TX + 4YZ

18, 2

Express the resultant vector as a linear combination of unit vectors i and j.

9) f = 7i - 4jv = 5i - 8jFind: 6f - 7v

7i + 32j

Draw a diagram to illustrate the horizontal and vertical components of the vector. Then findthe value of each component.

10) m = 22, 289°

m y

x

Horizontal: 7.16Vertical: -20.8

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-3-

Draw a vector diagram to find the resultant of each pair of vectors using the triangle method. Then state the magnitude and direction angle of the resultant.

11) m = 11, 3 n = 9, -12

m

n

m + n

21.93; 335.77°

12) a = -3, 4 b = 3, 13

a

b

a + b

17; 90°

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-4-

13) m = -20, -1 n = 8, 15

m

nm + n

18.44; 130.6°

14) t = -15, 5 u = 4, -10

t

u

t + u

12.08; 204.44°