MATH 2D Study Guide - Midterm Guide: Vector Projection, Parallelogram, Academic Dishonesty
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MATH 2D Full Course Notes
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Seat: there are 6 problems, of unequal weight, for a total of 100 points, present your work as clearly as possible. 2(cid:126)v (cid:126)w = 2(cid:104)1, 1, 1(cid:105) (cid:104)1, 0, 1(cid:105) = (cid:104)2 1, 2 0, 2 1(cid:105) = i 2 j + 3 k (b) |(cid:126)v| and | (cid:126)w|, | (cid:126)w| =(cid:112)12 + 02 + ( 1)2 = 2 (c) (cid:126)v (cid:126)w, (cid:126)v (cid:126)w = (1)(1) + ( 1)(0) + (1)( 1) = 0 (d) the angle between (cid:126)v and (cid:126)w. 2 (e) the area of the parallelogram spanned by (cid:126)v and (cid:126)w, and. Since these two vectors make a right angle, the parallelogram they span is a rectangle, whose area is therefore. 6. (you could instead use the more general formula that the area of this parallelogram is. |(cid:126)v (cid:126)w|; you could then use the fact that |(cid:126)v (cid:126)w| = |(cid:126)v|| (cid:126)w| sin .
