MATH 215 Midterm: exam1w03sol
Document Summary
Consider the points a(1, 3, 2), b(3, 1, 1), c( 4, 9, 8), and d( 2, 4, 4). (a 5 pts. ) Find an equation of the plane containing the points a, b, and c. To write down an equation of the plane, we need to know a point on the plane (any of a, b, or. In this problem we can easily nd two vectors in the plane, for example, Ab = h2, 2, 3i and ac = h 5, 6, 6i. Then their cross-product will be perpendicular to the plane: n = ab ac = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) i. 6x + 3y 2z = 6(1) + 3( 3) 2(2) 6x + 3y 2z = 6(3) + 3( 1) 2( 1) 6x + 3y 2z = 6( 4) + 3( 9) 2(8) = 19 taking p0 = a taking p0 = b taking p0 = c (b 5 pts. )
