My Math Forum Vectors Cross Product

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 February 29th, 2012, 08:24 AM #1 Senior Member   Joined: Sep 2011 From: New York, NY Posts: 333 Thanks: 0 Vectors Cross Product I am a little confused about the first one. I thought you would just take the coefficients of the x,y,z in both equations, and cross them. Knowing that the cross product of two vectors is a vector orthogonal to both vectors. eg: $\langle 1, 1, 1 \rangle \times \langle 2, -1, -1 \rangle$ BUT the tutor at school told me that you have to take two vectors that satisfy the equations and cross those vectors. Eg: $\langle 1, -1, 1 \rangle \times \langle 1, 1, 0 \rangle$ can some one please help me out with this? Separately, for the third question, I think to find the intersection of the two planes you just set the two equations equal to each other and solve. is that correct. $x+y+z=2x-y-z$ or no because you have two equations and three variables??? Help with either would be appreciated!
 February 29th, 2012, 03:57 PM #2 Global Moderator   Joined: May 2007 Posts: 6,216 Thanks: 493 Re: Vectors Cross Product The normals are obtained as you described, but you need to adjust the lengths to be 1. The angle can be gotten quickly by observing that the dot product of the normals = 0, so the planes must be perpendicular. The cross product of the normals points along the line of intersection. To get the line you need to get one point on the line, so the line is given by this point plus a scalar parameter multiplying that cross product. I don't understand what the tutor was driving at.

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