1. Sullivan Algebra and Trigonometry: Section 10.5
Objectives of this Section
Find the Dot Product of Two Vectors
Find the Angle Between Two Vectors
Determine Whether Two Vectors and Parallel or Orthogonal
Decompose a Vector into Two Orthogonal Vectors
Compute Work

3. Properties of Dot Product
If u, v, and w are vectors, then
Commutative Property
Distributive Property

4. Angle between Vectors

7. Determine whether the vectors v = -3i + 2j and w = -9i + 6j are parallel.
The vectors are parallel since w = 3v.

8. Two vectors v and w are orthogonal if and only if
Determine whether the vectors v = 4i - j and w = 2i + 8j are orthogonal.
The vectors v and w are orthogonal.

9. y
w = 2i + 8j x
v = 4i - j

14. The work W done by a constant force F in moving an object from A to B is defined as

15. Find the work done by a force of 30 pounds acting in the direction 3i + j in moving an object 20 feet from (0, 0) to (20, 0).
(3, 1)
(20, 0)