MATH 126 Midterm: MATH 126 UW Midterm 1 Spring 09conroyExIHans
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1. (a) find the equation of the plane p containing the point (1,2,3) which is parallel to the plane containing the points (0,3,4), (3,2,1), and (5,4,2). We rst nd two vectors extending between two pairs of points given. Two such vectors are h3, 1, 3i and h5, 1, 2i. Taking their cross product we have the vector h5, 9, 8i. This is the normal vector to the plane which is parallel to the plane p , and hence is the normal vector for the plane p . Since p contains the point (1, 2, 3), an equation for p is which can be, optionally, simpli ed to. 5(x 1) 9(y 2) + 8(z 3) = 0. 5x 9y + 8x = 11. (b) give an example of a line contained in plane p . There are very many reasonable approaches to this problem.
