Accelerated Math III Practice
Name____________________
Scalar and Vector Projections, etc.
Period_____Date___________
The scalar projection of a onto b is the length of the component of a in b’s direction. A
vector with that length in b’s direction is called the vector projection (vp). The component
of a that is perpendicular to b is called the orthogonal component (op). Remember that
the sum of the vector projection and the orthogonal component equals the original vector
a. In other words, vp + op = a .
I. For each of the following,
A) Find the scalar projection of a onto b
B) Find the vector projection of a onto b
C) Find the orthogonal component of the vector projection.
1. a = 5i + 12j and b = 8i + 6j
2. a = -5i + 12j and b = 8i + 6j
3. a = 8i + 6j and b = 5i + 12j
4. a = -8i + 6j and b = 5i + 12j
II. Find A) the scalar projection of a onto b and B) the length of the orthogonal
component.
5. |a| = 9, |b| = 10 and the angle between them is 120º
6. |a| = 8, |b| = 12 and the angle between them is 75º
III. A boy is pulling a wagon and a dog, exerting a
force of about 100 pounds. If he pulls at a constant
rate and the angle that the handle makes with the
ground is about 50º, how much of the force is moving
the wagon forward?
IV. If A has coordinates (4, 10), B has coordinates (12, 2) and C has coordinates (-2, 4),
1. Write vector AB. __________
2. Write vector BA. __________
3. Find |AC|. ___________
4. Locate point D if AB = CD? ___________
5. Write a unit vector in the same direction as AC. __________________
6. Write a vector equation of the line BC. __________________________
7. Locate coordinates of the point that is 2/3 of the way from B to C.____________
8. Write the vector equation of the line parallel to AB through C. _________________
9. Write the degree measure of the angle that AB makes with AC. ____________
10. Write the scalar projection of AB onto 4i - 3j.______________
11. Write the vector projection of AB onto 4i – 3j. ________________
12. Write the orthogonal component of this vector projection._________________
13. With which part of vectors do you feel confident?
14. With which part of vectors do you still have problems?