quiz2sol - equations obtained from the planes. This would...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 251, Spring 2008, Quiz 2 Solutions You are given the following equations: ( plane 1) P 1 : x + y + z = 1 ( plane 2) P 2 : x - y + z = 1 ( line ) L : x = 3 + 2 t ; y = 2 - 3 t ; z = 1 - 4 t Find the equation of a plane that contains the line of intersection of P 1 and P 2 and the point of intersection of P 2 and L . Does your answer look familiar? If yes, justify. Please draw an approximate picture of the problem to get full credit. Solution: For this one there was an easy solution. If you drew a picture, you would have realized that plane P 2 was going through both the line of intersection and the point specified. Hence P 2 is the right answer! The longer way to do this was: For the line of intersection the cross product of the normal vectors of both the planes would give the direction vector of the line, i.e < 1 , 1 , 1 > × < 1 , - 1 , 1 > = < 2 , 0 , 2 > . A point on this line can be obtained by setting z = 0 and solving the
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: equations obtained from the planes. This would yeild the point M = (1 , , 0). The point of intersection of P 2 and L is given by plugging in the expressions for x, y, z from L into the equation of the plane which gives that t =-1 and the required point is N = (1 , 5 , 5). Then the normal vector of the plane you are trying to find is given by the cross product of the direction vector of the line and the vector ~ NM which is < 1 ,-1 , 1 > . You also have a point of the plane and so the equation would turn out to be that of P 2. I think almost all gave up after finding P 1 ∩ P 2 and P 2 ∩ L . This problem was equivalent to two homework problems put together but I think it should have been doable in 25 min. 1...
View Full Document

This note was uploaded on 08/10/2008 for the course MATH 251 taught by Professor Beck during the Spring '08 term at Rutgers.

Ask a homework question - tutors are online