The Dot Product

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 (? 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 ? 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.