infinite precalculus - dot products and unit vector notes€¦ · precalculus dot products and unit...
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Worksheet by Kuta Software LLC
Precalculus
Dot Products and Unit Vector Notes
Name___________________________________
Date________________ Period____
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-1-
Find the dot product of the given vectors.
1) u = -7, -9v = 3, -2
2) u = 4, -2v = 4, -6
Find the measure of the angle between the two vectors.
3) u = -8i - 3jv = -2i - 4j
4) u = 9iv = -6j
5) u = 2, -9v = -4, 18
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Worksheet by Kuta Software LLC
-2-
State if the two vectors are parallel, orthogonal, or neither.
6) u = 5i - 35jv = -i + 7j 7) u =
3
2i - 3j
v = 3i - 6j
8) u = 18i - 18jv = 6i + j
9) u = 2i + 3j
v = -3
2i + j
Find the component form of the resultant vector.
10) Given: T = (4, 4) X = (2, 6)Unit vector in the direction of TX
11) Given: P = (-8, -5) Q = (-6, -6)Unit vector in the opposite direction of PQ
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Worksheet by Kuta Software LLC
-3-
Express the resultant vector as a linear combination of unit vectors i and j.
12) f = 4, 198°Unit vector in the direction of f
13) u = 22, 115°Unit vector in the direction of u
Find the magnitude and direction angle of the resultant vector.
14) Given: T = (5, 7) X = (-5, 6) Y = (6, -5) Z = (-7, 6)Find: TX - YZ
15) Given: P = (0, 7) Q = (4, 2)Unit vector in the opposite direction of PQ
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Worksheet by Kuta Software LLC
Precalculus
Dot Products and Unit Vector Notes
Name___________________________________
Date________________ Period____
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-1-
Find the dot product of the given vectors.
1) u = -7, -9v = 3, -2
-3
2) u = 4, -2v = 4, -6
28
Find the measure of the angle between the two vectors.
3) u = -8i - 3jv = -2i - 4j
42.88°
4) u = 9iv = -6j
90°
5) u = 2, -9v = -4, 18
180°
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Worksheet by Kuta Software LLC
-2-
State if the two vectors are parallel, orthogonal, or neither.
6) u = 5i - 35jv = -i + 7j
Parallel
7) u = 3
2i - 3j
v = 3i - 6j
Parallel
8) u = 18i - 18jv = 6i + j
Neither
9) u = 2i + 3j
v = -3
2i + j
Orthogonal
Find the component form of the resultant vector.
10) Given: T = (4, 4) X = (2, 6)Unit vector in the direction of TX
-2
2,
2
2
11) Given: P = (-8, -5) Q = (-6, -6)Unit vector in the opposite direction of PQ
-2 5
5,
5
5
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Worksheet by Kuta Software LLC
-3-
Express the resultant vector as a linear combination of unit vectors i and j.
12) f = 4, 198°Unit vector in the direction of f
-0.95i - 0.31j
13) u = 22, 115°Unit vector in the direction of u
-0.42i + 0.91j
Find the magnitude and direction angle of the resultant vector.
14) Given: T = (5, 7) X = (-5, 6) Y = (6, -5) Z = (-7, 6)Find: TX - YZ
3 17 » 12.369; 284.04°
15) Given: P = (0, 7) Q = (4, 2)Unit vector in the opposite direction of PQ
128.66°