assign2_soln

assign2_soln - Math 136 Assignment 2 Solutions 1. Let ~u =...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 136 Assignment 2 Solutions 1. Let ~u = 3 2- 2 , and ~v = 1 3- 1 . a) Find a unit vector in the direction of ~u . Solution: u = ~u k ~u k = 1 9+4+4 3 2- 2 = 1 17 3 2- 2 . b) Determine ~u ~v . Are ~u and ~v orthogonal? Solution: ~u ~v = 3(1) + 2(3) + (- 2)(- 1) = 11. Since ~u ~v 6 = ~ 0, they are not orthogonal. 2. a) Let ~u = 7 1- 1 and ~v = - 1 3- 3 . Calculate proj ~v ~u and perp ~v ~u . Solution: proj ~v ~u = ~u ~v k ~v k 2 ~v =- 1 19 - 1 3- 3 = 1 / 19- 3 / 19 3 / 19 perp ~v ~u = ~u- proj ~v ~u = 7 1- 1 - 1 / 19- 3 / 19 3 / 19 = 132 / 19 22 / 19- 22 / 19 . b) Let ~u = 2- 1 3- 4 and ~v = 1 1 . Calculate proj ~v ~u and perp ~v ~u . Solution: proj ~v ~u = ~u ~v k ~v k 2 ~v =- 2 2 1 1 = - 1- 1 perp ~v ~u = ~u- proj ~v ~u...
View Full Document

This note was uploaded on 11/25/2010 for the course MATH 136 taught by Professor All during the Spring '08 term at Waterloo.

Page1 / 4

assign2_soln - Math 136 Assignment 2 Solutions 1. Let ~u =...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online