MAT-2130 Midterm: MATH 2130 App State Fall2011 Test1
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|u| p12 + ( 2)2 + 22h1, 2, 2i = (b) find the volume of the parallelepiped spanned by u, v, and w. I"ll do the later. u v = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) i j. So the volume is |(u v) w| = |h0, 3, 3i h0, 1, 1i| = | 6| = 6. = (( 2)( 1) (1)(2))i ((1)( 1) (1)(2))j + ((1)(1) (1)( 2))k = h0, 3, 3i (c) find the angle between u and v (don"t worry about evaluating inverse trigonometric functions). Note that |u| = p12 + ( 2)2 + 22 = 9 = 3, |v| = p12 + 12 + ( 1)2 = 3, and u v = (1)(1) + ( 2)(1) + (2)( 1) = 3. Is this angle right, acute, or obtuse (circle your answer. ) A parallel line"s direction vector should be parallel to the direction vector of r(t) that is r (t) = h2, 1, 3i.
