# 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

,

,

Create your own worksheets like this one with Infinite Precalculus. Free trial available at

-2-

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Worksheet by Kuta Software LLC

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