MAT-2130 Midterm: MATH 2130 App State Fall2012 Test1
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Be sure to show your work: (17 points) let u = h1, 2, 3i, v = h 1, 0, 1i, and w = h2, 1, 1i. (a) find the area of the parallelogram spanned by v and w. The area of a parallelogram is given by the length of the cross product of the vectors which span its sides. i. Answer: the area of the parallelogram is |v w| =p( 1)2 + 32 + ( 1)2 = 11 . (b) find the angle between v and w (don"t worry about evaluating inverse trigonometric functions). |v||w|(cid:19) = arccos ( 1)2 + 0(1) + 1(1) p( 1)2 + 02 + 12 22 + 12 + 12! Notice that since v w = 1 < 0, we have that is obtuse. Is this angle obtuse or right, acute, (circle your answer. ) (c) find the volume of the parallelepiped spanned by u, v, and w.
