1. The Dot Product Sections 6.7

2. Objectives Calculate the dot product of two vectors. Calculate the angle between two vectors. Use the dot product to determine if two vectors are orthogonal, parallel, or neither.

3. Vocabulary dot product orthogonal parallel

4. Formulas Dot Product of and OR Angle between two vectors (θ is the smallest non-negative angle between the two vectors) and

5. Compute the dot product of each pair of vectors:

6. Given the vectors u = 8i + 8j and v = —10i + 11j find the following.

7. Given the vectors u = 8i + 8j, v = —10i + 11j, and w = 9i + 7j find the following.

8. Find the angle θ in degrees measured between the vectors u = 10i + 3j and v = 1i — 7j.

9. Determine if the pair of vectors is orthogonal, parallel, or neither.