Two-Dimensional Vector Dot Products
Kuta Software - Infinite Precalculus
Two-Dimensional Vector Dot Products
Find the dot product of the given vectors.
1) u , v ,
Name___________________________________ Date________________ Period____
2) u i j v i j
3)
(, )
4)
(, )
(, )
(, )
State if the two vectors are parallel, orthogonal, or neither.
5) u , v ,
6) u i j v i j
Find the measure of the angle between the two vectors.
7)
8)
(, )
(, )
(, ) (, )
-1-
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Worksheet by Kuta Software LLC
9) u , v ,
10) u j v i j
Find the projection of u onto v.
11) u , v ,
12) u i j v i j
Find the projection of u onto v. Then write u as the sum of two orthogonal vectors.
13) u , v ,
-2-
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Precalculus
Two-Dimensional Vector Dot Products
Find the dot product of the given vectors.
1) u , v ,
Name___________________________________ Date________________ Period____
2) u i j v i j
3)
(, )
4)
(, )
(, )
(, )
State if the two vectors are parallel, orthogonal, or neither.
5) u , v ,
6) u i j v i j
Neither
Orthogonal
Find the measure of the angle between the two vectors.
7)
(, )
8)
(, )
(, )
142.13?
132.88?
(, )
-1-
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Worksheet by Kuta Software LLC
9) u , v ,
59.04?
10) u j v i j
77.47?
Find the projection of u onto v.
11) u , v , ,
12) u i j v i j
,
Find the projection of u onto v. Then write u as the sum of two orthogonal vectors.
13) u , v ,
,
u
,
,
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-2-
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Worksheet by Kuta Software LLC
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