The transformation T in R3 given by x = au + bv + cw, y = dv + fw, z = w, where

Question

The transformation T in R3 given by x = au + bv + cw, y = dv + fw, z = w, where a, b, c, and f are positive real numbers, is one of many possible shear transformations in R3. Let S be the unit cube {(u, v, w): 0 u 1, 0 v 1, 0 w 1}. Let D = T(S) be the image of S. Explain the effect of T on S. Choose the correct answer below. S is stretched in the positive w-direction but not in the u- and v-directions. The amount of stretching increases with u and v. S is stretched in the positive v- and w-directions but not in the u-direction. The amount of stretching increases with u and v. S is stretched in the positive u- and v-directions but not in the w-direction. The amount of stretching increases with u and v. S is stretched in the negative u- and v-directions but not in the w-direction. The amount of stretching increases with u and v. Compute the Jacobian of T. j(u, v, w) = Find the volume of D. Volume = Assuming a constant density, find the center of mass of D. Assuming a constant density, find the center of mass of D. The center of mass of D is

Explanation / Answer

a) answer is option c b) answer is

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