MAT-2130 Midterm: MATH 2130 App State Spring2018 Test1
Document Summary
Name: answer key: (24 points) vector basics: let u = h 1, 1, 1i, v = h1, 0, 3i, and w = h2, 1, 2i. (a) compute the area of the parallelogram spanned by v and w. The area of the parallelogram spanned by v and w is given by |v w|. First, we compute the cross product. h1, 0, 3i h2, 1, 2i = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) Then the area of the parallelogram is |v w| = |h3, 4, 1i| = p32 + 42 + ( 1)2 = 9 + 16 + 1 = 26 . 0 (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) k = h0(2) ( 1)3, (1(2) 2(3)), 1( 1) 2(0)i = h3, 4, 1i (b) find the volume of the parallelepiped spanned by u, v, and w. The volume of the parallelepiped spanned by u, v, and w is given by the absolute value of the triple scalar product:
