MAT-2130 Midterm: MATH 2130 App State H Fall2007 Exam1
Document Summary
Math 251h fall 2007 exam #1 answer key: (12 points): let p , q, and r be points in r3. Using only dot products, cross products, and magnitudes, explain how to tell if (a) ~p q and ~p r are orthogonal. ~p q and ~p r are orthogonal if and only if ~p q ~p r = 0. (b) ~p q and ~p r are parallel. If p , q, r are on the same line, then ~p q and ~p r must be parallel. R are colinear if and only if ~p q ~p r = ~0: (14 points): consider the following lines: Line l1 : x(t) = 1 + t y(t) = 1 + 2t z(t) = 0 t. L1 is parallel to the vector h1, 2, 1i, and l2 is parallel to the vector h 2, 4, 2i. It"s easy to see that h 2, 4, 2i = 2h1, 2, 1i.
