Page 8 - AP Unit 2 Vectors Student Binder_Neat

AP 2.4 Finding vector in same direction with given magnitude
Name __________________________________________________ Date _____ Class _______

Find the vector v with the given magnitude and the same direction as u.

Magnitude Direction

1. ‖ ‖ =8 u =〈5, 6〉
2. ‖ ‖ =3 u =〈4, −4〉
3. ‖ ‖ =7 u =3 + 4
4. ‖ ‖ =10 u =2 − 3
5. ‖ ‖ =8 u =−2
6. ‖ ‖ =4 u =5

For 7-10, the initial and terminal points of a vector are given. Write the vector as a linear combination of
the standard unit vectors i and j. Then state direction angle.

Initial Point Terminal Point Linear Combination Component form Direction angle

7. (-3, 1) (4,5)
8. (0, -2) (3, 6)
9. (-1, -5) (2,3)
10. (-6, 4) (0, 1)

More Operations. In exervises 11-16, find the component form of v and sketch the specified vector
operations geometrically, where = 2 − and = + 2 .

2
3
11. = 13. = 14. = + 2
2 3

1
15. = − + 16. = (3 + ) 17. = 2 − 2
2

In exercises 18-23, find the component form of v given its magnitude and the angle it makes with the
positive x-axis.

Magnitude Angle
18. ‖ ‖ = 3 = 0°
19. ‖ ‖ = 1 = 45°

20. ‖ ‖ = 3√2 = 150°
21. ‖ ‖ = 4√3 = 90°
22. ‖ ‖ = 2 = 190°
23. ‖ ‖ = 3 = 272°
24. ‖ ‖ = 12 = 312°

nd
25. Explain how using the unit vector method and using the 2 tan method results in the same answer.
Record this response in your composition books, along with examples.