Page 9 - AP Unit 2 Vectors Student Binder_Neat
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AP 2.5 Dot Product and Angle Between Vectors
Name ____________________________________________ Date ____________ Class___-
Fill in the blank.
1. The ___________ of two vectors yields a scalar, rather than a vector.
2. If is the angle between two nonzero vectors u and v, then cos = _______________.
3. The vectors u and v are ____________ if ∙ = 0.
State the dot product of u and v.
4. = 〈6, 3〉 = 〈2, −4〉 5. = 〈−4, 1〉 = 〈2, −3〉
6. = 5 + = 3 − 7. = 3 + 2 = −2 +
For 8-13, use the vectors = 〈2, 2〉 = 〈−3, 4〉, and = 〈1, −4〉 to find the indicated quantity. State
whether the result is a vector or a scalar.
8. ∙ 9. ∙ 10. ∙ 2 11. 4 ∙ 12. (3 ∙ ) 13. ( ∙ 2 )
For exercises 14-19, use the dot product to find the magnitude of u.
14. = 〈−5, 12〉 15. = 〈2, −4〉 16. = 20 + 25
17. = 6 − 10 18. = −4 19. = 9
20)
a) Find the dot product of the two vectors. b) Find the angle between the two vectors.
a = −2,5 ,b = 3,6 a = 8i− 3 j,b = 2i − 7 j
21) Show that the two vectors are orthogonal.
a = 4,−1 ,b = 2,8
22) Show that the vectors are parallel., and determine whether they have the same direction or opposite directions.
5
a = i +10j,b = 3i+18 j a = 1,−4 ,b = −2,8
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