MAC-2313 Final: MAC2313 final-key
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An answer with no work receives no credit. You may use the back of a page if you need more space for a problem. Calculus iii (mac2313-13: circle true or false. Page 2 of 8 (a) (2 points) true false u (v w) = (w v) u for all u, v, and w in r3. Hint: look at a vector connecting the planes. Solution: we pick two arbitrary points p = (0, 0, 0) and q = (0, 0, 1/9) on the rst and second plane, respectively. The magnitude of the component of the vector a = ~p q = (which connects the two planes) along the normal vector n = . (which is the same for both planes) gives the distance between the planes. Since |n| = 1 + 4 + 9 = 14 and a n = 3/9 = 1/3, we have. N | = |a un| = (cid:12)(cid:12)(cid:12)(cid:12) a .