Lesson three
Assignment
Name:
r
r
r
In 1-3, let u = (5, 10), v = (-1, 3), and w = (4, 7), and compute.
r r
1. u  v
 r r r
2. ( u  v )w



r
r r r
3. (u + v )  (v - w )

In 4-6, find the measure of the angle between the two vectors.



4. (-1, 1) and (4, 2)
5. (0, 8) and (-4, 0)
6. [18, 63º] and [42, 172º]
r
r
7. Show that v = (20, 18) and u = (-6, 10) are not orthogonal.
r

r
r r r r
r r r r
8. If u and v are vectors in a plane, prove the ( u + v )  ( u - v ) = u  u - v  v .

 


r
r  
In 9-11, determine whether u and v are perpendicular, parallel, or neither.
r
r
9. u = (-2, 1), v = (10, -5)

r
r 
10. u = (3, -4), v = (6, 2)



r 
r
11. u = (7, -3), v = (-6, -14)

r
In 12 and 13, let v = (4, -4).
Write avector equation for the line through P = (-1, 8) that is
r
12. parallel
to
.
v

r
13. perpendicular to v .

