http://www.ck12.org Chapter 7. Vectors
u·v
|u||v|=cosθ
< 3 ,√ 5 >·< 2 , 8 >
34 ·√ 68 =cosθ
√^6 +^35
34 ·√ 68 =cosθ
cos−^1( 41
√ 34 ·√ 68
)
=θ
31. 49 ≈θPractice
Find the dot product for each of the following pairs of vectors.
1.< 2 , 6 >·<− 3 , 5 >
2.< 5 ,− 1 >·< 4 , 4 >
3.<− 3 ,− 4 >·< 2 , 2 >
4.< 3 , 1 >·< 6 , 3 >
5.<− 1 , 4 >·< 2 , 9 >
Find the angle between each pair of vectors below.
6.< 2 , 6 >·<− 3 , 5 >
7.< 5 ,− 1 >·< 4 , 4 >
8.<− 3 ,− 4 >·< 2 , 2 >
9.< 3 , 1 >·< 6 , 3 >
10.<− 1 , 4 >·< 2 , 9 >
- What isv·v?
- How can you use the dot product to find the magnitude of a vector?
- What is 0·v?
- Show that(cu)·v=u·(cv)wherecis a constant.
- Show that< 2 , 3 >is perpendicular to< 1. 5 ,− 1 >.