(d) Consider the parallelepiped P in R³ whose adjacent sides are (0, 4, 0), (3, 0, 0) and (-1, 1, k), where ke Z. If the volume of P is 180, find the two possible values of k.

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Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
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(d) Consider the parallelepiped P in R³ whose adjacent sides are (0, 4, 0), (3, 0, 0) and (-1, 1, k), where k = Z. If the volume of P is 180,
find the two possible values of k.
k =
k=
(e) Given that the vectors u = (1, 1, 1, 1, 1) and = (-1, k, 1, k, 6) are orthogonal, find the magnitude of . Give your answer in surd form.
15
||
Transcribed Image Text:(d) Consider the parallelepiped P in R³ whose adjacent sides are (0, 4, 0), (3, 0, 0) and (-1, 1, k), where k = Z. If the volume of P is 180, find the two possible values of k. k = k= (e) Given that the vectors u = (1, 1, 1, 1, 1) and = (-1, k, 1, k, 6) are orthogonal, find the magnitude of . Give your answer in surd form. 15 ||
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