MAT-2130 Midterm: MATH 2130 App State summer2016 Test1
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Name: (20 points) vector basics: let v = h3, 1, 2i and w = h2, 1, 1i. (a) find a unit vector perpendicular to both v and w. First, the cross product v w will give us a vector perpendicular to both v and w. But we want a unit vector that"s perpendicular to v and w, so we need to normalize the cross product. v w =(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) 5 3h 1, 7, 5i is a unit vector which is perpendicular to both v and w. j +(cid:12)(cid:12)(cid:12)(cid:12) = i + 7j + 5k (b) compute projv(w) = v w. 14h3, 1, 2i (c) find the angle between v and w (don"t worry about evaluating inverse trig. functions). Recall that v w = |v||w| cos( ) where is the angle between v and w. so noting that v w = 3, |v| = 14, |w| =q22 + 12 + ( 1)2 = 6, and solving for we get:
