# SOL11 - Thevalingam Donald – Homework 11 – Due midnight...

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

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: Thevalingam, Donald – Homework 11 – Due: Dec 15 2006, midnight – Inst: Eslami 1 This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Vector ~ A has components A x =- 7 . 7 , A y = 8 . 5 , A z = 4 , while vector ~ B has components B x = 3 . 7 , B y =- 4 . 8 , B z = 6 . 4 . What is the angle θ AB between these vec- tors? (Answer between 0 ◦ and 180 ◦ .) Correct answer: 114 . 084 ◦ . Explanation: Note: The magnitude of vector ~ X is k X k . Consider two formulae for the scalar prod- uct ~ A · ~ B of two vectors: ~ A · ~ B = A x B x + A y B y + A z B z (1) in terms of the two vectors’ components, and also ~ A · ~ B = k ~ A kk ~ B k cos θ AB (2) in term of their magnitudes and the angle be- tween them. Given the data, we immediately calculate k ~ A k = q A 2 x + A 2 y + A 2 z = 12 . 1466 , (3) k ~ B k = q B 2 x + B 2 y + B 2 z = 8 . 81419 , (4) and using eq. (1), ~ A · ~ B =- 43 . 69 . (5) Hence, according to eq. (2), cos θ AB = ~ A · ~ B k ~ A kk ~ B k =- . 408079 (6) and therefore θ AB = arccos(- . 408079) = 114 . 084 ◦ . (7) Two vectors always lie in a plane. When these two vectors are plotted in this plane, we have A B 1 1 4 . 8 4 ◦ keywords: 002 (part 1 of 2) 10 points Consider the two vectors ~ M = ( a,b ) = a ˆ ı + b ˆ and ~ N = ( c,d ) = c ˆ ı + d ˆ , where a = 4, b = 4, c = 3, and d =- 3. a and c represent the x-displacement and b and d represent the y- displacement in a Cartesian xy co-ordinate system. Note: ˆ ı and ˆ represent unit vectors ( i.e. vectors of length 1) in the x and y directions, respectively. What is the value of the scalar product ~ N · ~ N ? Correct answer: 18 . Explanation: Take the scalar products of the x- and y- displacement of ~ N and ~ N individually ~ N · ~ N = ( c ˆ ı + d ˆ ) · ( c ˆ ı + d ˆ ) = c 2 (ˆ ı · ˆ ı ) + dc (ˆ · ˆ ı ) + cd (ˆ ı · ˆ ) + d 2 (ˆ · ˆ ) = c 2 + d 2 = (3) 2 + (- 3) 2 = 18 . since ˆ ı ⊥ ˆ , we have ˆ ı · ˆ ı = 1, ˆ · ˆ ı = 0, ˆ ı · ˆ = 0, and ˆ · ˆ = 1....
View Full Document

## This note was uploaded on 03/04/2010 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas.

### Page1 / 5

SOL11 - Thevalingam Donald – Homework 11 – Due midnight...

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

View Full Document
Ask a homework question - tutors are online