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Show that the line of intersection of the planes\[x+2yz=2\mbox{ and } 3x+2y+2z=7\]is parallel to the line \[\langle x,y,x \rangle = \langle 1+6t,35t,24t \rangle\]
 one year ago
 one year ago
Show that the line of intersection of the planes\[x+2yz=2\mbox{ and } 3x+2y+2z=7\]is parallel to the line \[\langle x,y,x \rangle = \langle 1+6t,35t,24t \rangle\]
 one year ago
 one year ago

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richywBest ResponseYou've already chosen the best response.1
my attempt at a solution. First I found normal vectors to the planes. \[\vec{n}=\langle 1,2,1 \rangle\]\[\vec{m}=\langle 3,2,2\rangle\]then the cross product to get the vector parallel to that.\[\vec{n}\times \vec{m} = \langle 6, 5, 4 \rangle\]
 one year ago

richywBest ResponseYou've already chosen the best response.1
so wouldn't this be the direction of the line formed by the intersection of the two planes?
 one year ago

richywBest ResponseYou've already chosen the best response.1
so maybe what I am doing wrong is finding the direction of the second line. how would I do this? find two points on the line and then use the displacement vector?
 one year ago

richywBest ResponseYou've already chosen the best response.1
NICE just figured it out myself, question closed.
 one year ago
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