MAT-2130 Midterm: MATH 2130 App State Spring2012 Test1
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Be sure to show your work! projv(u) = v u v. |r (t)| r (t) = (cid:18) r (t) r (t) (cid:19) n(t) 7(cid:29) (b) find the angle between v and w (don"t worry about evaluating inverse trigonometric functions). Recall that v w = kvkkwk cos( ) where is the angle between the vectors. We already calculated that v w = 5 and kwk = 14. In addition, kvk = p(2)2 + ( 1)2 + (1)2 = 6. = arccos(cid:18) v w kvkkwk(cid:19) = arccos(cid:18) 5. The angle between v and w is obtuse because v w = 5 < 0. The area of this parallelogram is k ~p q ~p rk = (cid:13)(cid:13)(cid:13)(cid:13)(cid:13)(cid:13) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) i. The area of the triangle is half that of the parallelogram. Answer: the area of p qr is 1. Determine if 1 and 2 are the same, parallel, intersecting, or skew. 2(t) = h1, 2, 3i and not multiples of each other.
