MAT-2130 Midterm: MATH 2130 App State Spring2016 Test1
Document Summary
Be sure to show your work: (20 points) vector basics: let u = h2, 2, 1i, v = h 1, 3, 1i, and w = h 1, 1, 0i. (a) find the volume of the parallelepiped spanned by u, v, and w. Recall that the volume of a parallelepiped is given by the absolute value of the triple scalar product. This can be computed directly by evaluating a 3 3 determinant (done quickly with the 3 3 determinant trick) or by computing a cross product followed by a dot product. i j. = h( 2)1 (3)1, ((2)1 ( 1)1), (2)3 ( 1)( 2)i = h 5, 3, 4i (u v) w = h 5, 3, 4i h 1, 1, 0i = ( 5)( 1) + ( 3)( 1) + 4(0) = 8. Alternatively, v w = h1, 1, 4i and so u (v w) = 8.
