assign1_soln

assign1_soln - Math 136 Assignment 1 Solutions 1. Compute...

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

View Full Document Right Arrow Icon
Math 136 Assignment 1 Solutions 1. Compute each of the following. a) (1 , 3 , 4) + ( - 1 , 1 , 2) Solution: (1 , 3 , 4) + ( - 1 , 1 , 2) = (0 , 4 , 6). b) 3( - 1 , 1 , - 2) - 2(2 , 0 , 3). Solution: 3( - 1 , 1 , - 2) - 2(2 , 0 , 3) = ( - 3 , 3 , - 6) + ( - 4 , 0 , - 6) = ( - 7 , 3 , - 12). 2. Determine the distance between P (2 , 1 , 1) and Q (1 , - 1 , 1). Solution: The distance is ± (1 , - 1 , 1) - (2 , 1 , 1) ± = ± ( - 1 , - 2 , 0) ± = ± ( - 1) 2 +( - 2) 2 +0 2 = 5. 3. Determine which of the following pairs of vectors is orthogonal. a) (2 , 1 , 1), ( - 2 , 1 , 3). Solution: We have (2 , 1 , 1) · ( - 2 , 1 , 3) = - 4 + 1 + 3 = 0 so they are orthogonal. b) ( - 1 , 3 , 6), (3 , - 1 , 0). Solution: We have ( - 1 , 3 , 6) · (3 , - 1 , 0) = - 3 - 3 + 0 = - 6 so they are not orthogonal. 4. Find an equation for the plane through P (3 , - 2 , 1) and parallel to x 1 - x 2 +2 x 3 = 4. Solution: Since the plane is parallel to x 1 - x 2 x 3 = 4 it must have normal vector ±n = (1 , - 1 , 2). Thus the equation of the plane is x 1 - x 2 x 3 = 1(3) - 1( - 2) + 2(1) = 7 . 5. For each of the following sets: i) Determine if the set is linearly dependent or linearly independent. Justify. ii) Describe geometrically the span of the set and give a simpli±ed vector equation which describes it.
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/30/2010 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.

Page1 / 3

assign1_soln - Math 136 Assignment 1 Solutions 1. Compute...

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