hw1.3.18

hw1.3.18 - c. This has no solution, so L is Neither...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
(week 3, continued) Problem 1.3.18: The line L passes through the point P = (1 , - 1 , 1) and has direction vector ± d = [2 , 3 , - 1] . For each of the following planes, determine whether L and the plane are parallel, perpendicular or neither. Solution: If the plane has normal vector ±n, the answer depends on whether ± d and ±n are parallel, perpendicular or neither. We explain below. (a) 2x+3y-z=1. Soln: ±n = [2 , 3 , - 1] and for ± d = [2 , 3 , - 1] ±n · ± d = [2 , 3 , - 1] · [2 , 3 , - 1] = 4 + 9 + 1 ± = 0 . This says that L is NOT Parallel to the plane. (why?) In fact, ±n = ± d, so L is Perpendicular to the plane. (b) 4 x - y + 5 z = 0 has ±n = [4 , - 1 , 5] and ±n · ± d = [4 , - 1 , 5] · [2 , 3 , - 1] = 8 - 3 - 5 = 0 , so L IS Parallel to this plane. (why?)
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 (c) x - y - z = 3 has ±n = [1 , - 1 , - 1] and ±n · ± d = [1 , - 1 , 1] · [2 , 3 , - 1] = 2 - 3 - 1 ± = 0 , so L isn’t parallel. Now we check c±n = ± d = [1 , - 1 , 1] , so c [1 , - 1 , 1] = [2 , 3 , - 1] , so we need c = 2 , - c = 3 and c = - 1 , all for the same
Background image of page 2
Background image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: c. This has no solution, so L is Neither parallel nor perpendicular to this plane. Last comments on Homework 2 (I hope!): From our text we have the statement Problem 1.2.34, Section 1.2, pg. 26: Find the projection of v onto u where u = [1 ,-1] , v = [3 ,-1] . We recall (from your homework papers) that proj u ( v ) was a vector in the direction of u = [1 ,-1] . As a clarication, we note Example, NOT Problem 1.2.34: Find the projection of b = [1 ,-1] onto a = [3 ,-1] , for which we found proj a ( b ) = 4 10 a = 2 5 [3 ,-1] . For emphasis, this vector a = [3 ,-1] was NOT the texts vector u (and WORSE, was the texts vector v . . . )....
View Full Document

Page1 / 3

hw1.3.18 - c. This has no solution, so L is Neither...

This preview shows document pages 1 - 3. Sign up to view the full document.

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