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Unformatted text preview: Chapter Review Exercises 443 We want to find the value of t for which the point ( x , y , z ) lies on the plane. We substitute the parametric equations in the equation of the plane and solve for t : 2 ( 3 t + 2 ) 3 1 + ( 7 t ) = 5 6 t + 4 3 7 t = 5 t = 4 t = 4 The point P of intersection of the line and the plane has the coordinates: x = 3 ( 4 ) + 2 = 10 , y = 1 , z = 7 ( 4 ) = 28 and thus, P = ( 10 , 1 , 28 ) . 47. Find the trace of the plane 3 x 2 y + 5 z = 4 in the xyplane. SOLUTION The xyplane has equation z = 0, therefore the intersection of the plane 3 x 2 y + 5 z = 4 with the xyplane must satisfy both z = 0 and the equation of the plane. Therefore the trace has the following equation: 3 x 2 y + 5 = 4 3 x 2 y = 4 We conclude that the trace of the plane in the xyplane is the line 3 x 2 y = 4 in the xyplane. 48. Find the intersection of the planes x + y + z = 1 and 3 x 2 y + z = 5. SOLUTION The line of intersection of the planes x + y + z = 1 and 3 x 2 y + z = 5 consists of all points that satisfy the equations of the two planes. Therefore, we must solve the following equations: x + y + z = 1 3 x 2 y + z = 5 The first equation implies y = 1 x z . Substituting in the second equation and solving for....
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This homework help was uploaded on 04/22/2008 for the course MATH 32A taught by Professor Gangliu during the Winter '08 term at UCLA.
 Winter '08
 GANGliu
 Equations, Parametric Equations

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