(a) Find the volume of the parallelepiped spanned by a = 4i + 2j − k, b = −i + 10j + 7k, a...

(a) Find the volume of the parallelepiped spanned by a = 4i + 2j − k, b = −i + 10j + 7k, and c = i − k.

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(b) Suppose that a in (a) is replaced by 8i + 4j − 2k. What is the volume of the resulting parallelepiped? What property of determinants does this illustrate?

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(c) Suppose that a, b, and c in (a) are replaced by 8i + 4j − 2k, −3i + 30j + 21k, and . Without evaluating a determinant, find the volume of the resulting parallelepiped.