MAT-2130 Midterm: MATH 2130 App State summer2015 Test1
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Name: answer key: (17 points) vector basics: let u = h2, 1, 1i, v = h3, 1, 2i, and w = h 1, 2, 2i. (a) compute the area of the parallelogram spanned by v and w. Be sure to show your work! v w = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) j. 1 2(cid:12)(cid:12)(cid:12)(cid:12) v w = h 6, 4, 7i j +(cid:12)(cid:12)(cid:12)(cid:12) 1 2(cid:12)(cid:12)(cid:12)(cid:12) k = (1( 2) 2(2))i (3( 2) ( 1)(2))j + (3(2) ( 1)1)k. The volume is | 15| = 15 . (c) find two vectors of length 5 which are parallel to w. So now we have a unit vector which points in the same direction as w. if we want a vector of length 5, we just need to scale this vector by 5 (chucking in a minus w. 1 sign will yield the second desired vector): p( 1)2 + 22 + ( 2)2h 1, 2, 2i =
