MTH 141 Midterm: MTH141 – F2008 Midterm2 (Solution)
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Mth 141, midterm test 2: (4) let a = (2, 1, 1) and b = ( 1, 2, 3) be points in r3. We need 0 = u v = 2 2k 1, so k = 1/2. (b) find a vector that is perpendicular to both u and w. The distance is simply ||u w|| =p(1 ( 1))2 + ( 2 0)2 + (1 2)2 = 3. (d) find the cosine of the angle between u and w. cos = u v. 30 (e) find a unit vector parallel to w. Use w/||w|| = ( 1/ 5, 0, 2/ 5: (4+4) let a = ( 1, 3, 2) and u = ( 1, 7, 3). (a) find the projection of u onto a (projau). projau = a = The easiest way is to recall that area = 1. 2||( 1, 5, 2) (2, 0, 3)|| = 1.
