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Unformatted text preview: y = t . Then x =2 t and z = 0. In other words, h x, y, z i = t h2 , 1 , i . Of course, other answers are also valid, for example, h x, y, z i = t h 2 ,1 , i + h4 , 2 , i . Alternatively, we could take the cross product of the two normals to the planes, h 1 , 2 , i and h , , 1 i to get a vector in the direction of the line. We also need a point on the line. The origin works since the plane passes through the origin. Alternatively, we could nd two points on the line, P and Q and then the line would be t P Q + Q . An obvious point is the origin. We can nd another by choosing any nonzero value for x or y ; for example, with x = 12, x + 2 y = 0 gives us y =6. Since we have z = 0 from the second plane, our point is (12 ,6 , 0)....
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This note was uploaded on 06/17/2009 for the course MATH 20C taught by Professor Helton during the Fall '08 term at UCSD.
 Fall '08
 Helton
 Math, Calculus

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