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©a `2d0X1d8g hK`uBtNaN uSNoZfKtKwba`rWeB NLmLiCS.V M aAVlll_ CrHiqgzhqtvs_ rrCems\eurGvLeCd_.x V XMAa]dNez VwmintMhJ lIPnTfqivntiBtveC `PIrieqcfaSlVcZuZlDuwsm.
Worksheet by Kuta Software LLC
Precalculus
Vector Operations Notes
Name___________________________________
Date________________ Period____
©a _2]0A1k8E \KjuGtyaL jSfoafat^wTaerwe_ ZLHLeCA.a a yA`lulq rrMiTgchKtesx ^rZeAsJeLrgvee\dy.
-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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Worksheet by Kuta Software LLC
-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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Worksheet by Kuta Software LLC
-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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Worksheet by Kuta Software LLC
-4-
13) m = -20, -1 n = 8, 15 14) t = -15, 5 u = 4, -10
©\ B2D0U1y8X uKnuutwaX zSzoQfNtgwPaArkeN vLtLFCX.f _ CAglcly er\iNgohVtTsK Qr_eosHeRrVvReJdt.T y VMzaLdJeU wwoigtDho fIonFfFiknFi]txeP HP\roeXcoaklsc`uHlxupsc.
Worksheet by Kuta Software LLC
Precalculus
Vector Operations Notes
Name___________________________________
Date________________ Period____
©G p2k0\1i8j kKZuRteac nSHoTfltbwZa_rOev PLpLZCP.g I aAclylM xrniIg^h^tjsd vrneysqeGrvv\eydi.
-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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Worksheet by Kuta Software LLC
-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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Worksheet by Kuta Software LLC
-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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Worksheet by Kuta Software LLC
-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°