Chapter 10: Q14P (page 517)
Short Answer
B is an axial vector.
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Chapter 10: Q14P (page 517)
B is an axial vector.
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Let be the tensor in . This is a -rank tensor and so has components. Most of the components are zero. Find the nonzero components and their values. Hint: See discussion after .
Bipolar.
Following what we did in equations (2.14) to (2.17), show that the direct product of a vector and a -rank tensor is a -rank tensor. Also show that the direct product of two -rank tensors is a -rank tensor. Generalize this to show that the direct product of two tensors of ranks m and n is a tensor of rank m + n .
Write out the sums for each value of and compare the discussion of .Hint: For example, if [or y in ], then the pressure across the face perpendicular to theaxis is , or, in the notation of (1.1), .
Verify Hints: In Figure , consider the projection of the slanted face of area onto the three unprimed coordinate planes. In each case, show that the projection angle is equal to an angle between the axis and one of the unprimed axes. Find the cosine of the angle from the matrix A in .
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