Question: Let D be a solid heat-conducting cube formed by the planes x = 0, x = 1, y = 0, y = 1, z =

Let D be a solid heat-conducting cube formed by the planes x = 0, x = 1, y = 0, y = 1, z = 0, and z = 1. The heat flow at every point of D is given by the constant vector Q = (0, 2, 1).

a. Through which faces of D does Q point into D?

b. Through which faces of D does Q point out of D?

c. On which faces of D is Q tangential to D (pointing neither in nor out of D)?

d. Find the scalar component of Q normal to the face x = 0.

e. Find the scalar component of Q normal to the face z = 1.

f. Find the scalar component of Q normal to the face y = 0.

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