MATH 230 Midterm: Test 1 spring 2009
15 Feb 2019
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Please do not write your name, instead write your netid: Question 1. (20 points) given the four points p = (1, 1, 0), q = (2, 1, 1), R = ( 1, 1, 3) and s = (2, 0, 3), nd: (a) (5pts) the projection of the vector. P r. (b) (6pts) the equation of the plane containing the points p , q and r. problem continued on next page. Page 3 of 9 (c) (5pts) the area of the triangle p qr. (d) (4pts) find the volume of the parallelepiped spanned by the vectors the vector. Question 2. (10 points) find parametric equations for the line l through (5, 1, 0) that is perpendicular to the plane 2x y + z = 1. Question 3. (18 points) (a) (6pts) determine whether the planes p1 : x + y + z = 1 and p2 : x y + z = 1 are parallel.
