{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

7.7_bzat4e

# 7.7_bzat4e - the picture at right there is force F which is...

This preview shows pages 1–20. Sign up to view the full content.

Section 7.7 The Dot Product

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The Dot Product of Two Vectors

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example If v=4i-2j and u=-2i+3j a. find v u b. find v v g g
The Angle between Two Vectors

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example Find the angle between v=2i-2j and w=-3i+5j. Round to the nearest tenth of a degree. θ -5 -4 -3 -2 -1 1 2 3 4 5 6 -5 -4 -3 -2 -1 1 2 3 4 5 x y θ

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Parallel and Orthogonal Vectors
0 .0 0 Two vectors are parallel when the angle between them is 0 or 180 . Two vectors are orthogonal if the angle between them is 90 . We say the vectors are orthogonal not perpendicular.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example Are the following two vectors orthogonal? u=2i-4j v=6i+3j

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Projection of a Vector Onto Another Vector
You know how to add two vectors to obtain a resultant vector. We now reverse this process to express a vector as the sum of two orthogonal vectors. By doing this you can determine how much force is appli 1 2 ed in a particular direction. As in

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: the picture at right there is force F which is pulling the boat down the ramp. F is the force pressing against the ramp. The resultant force F is gravity. Example If v=4i+3j and w=-3i+5j, find the projection of v onto w.-6-5-4-3-2-1 1 2 3 4 5 6 7-6-5-4-3-2-1 1 2 3 4 5 6 x y v w Work: An Application of the Dot Product Example 30 50 lbs An person pulls a sled with her dog on it along level ground by exerting a force of 50 pounds on a rope that makes an angle of 30 with the horizontal. How much work is done pulling the sled 100 feet? (a) (b) (c) (d) Find the angle between v and w. Round to the nearest tenth of a degree.v=i-j and w=2i+3j. 30 100.7 101.3 29.5 (a) (b) (c) (d) Find v (w+u) if v=i-j, w=2i+3j and u=-3i+j g 1 4 5---...
View Full Document

{[ snackBarMessage ]}

### Page1 / 20

7.7_bzat4e - the picture at right there is force F which is...

This preview shows document pages 1 - 20. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online