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MVC SHOW ALL WORK !! Sample Quiz #1 #1(5 pt's) Find the equation of the plane through (1,0,2) that is parallel to the xy-plane. Solution: z = 2 Any plane parallel to the xy-plane has equation z = constant. #2(5 pt's) Find the parametric equations of the line of intersection of the two planes given by: 2x – 3y + 4z = 2 and x + 4z = – 2 ( x 2) ( y 1) ( z 3) intersect the plane given by 2 2 4 3x 5 y z 2 . Explain/show work. #3(4 pts) Does the line given by MVC x 2t 1 #4(4 pt's) Find the angle between the line given by y t 1 and the plane given by z t 3 4x 2 y z 0 #5(8 pt’s) Let u , v , w R 3 and a R . Determine whether each statement is true or false. If true, prove it. If false, give an example that demonstrates it is false. a. a(u v ) au av b. MVC If u (v w) 0, then u , v , and w all lie in the same plane. x 2t 3 x 3t 1 #6(4 pt’s) Find the distance between the lines given by y t 1 and y 2t . z 3t 2 z t 2 MVC