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in Vector algebra by (36.4k points)

Find 3-dimensional vectors v1, v2, v3 satisfying v1.v1 = 4, v1.v2 = – 2 and v1.v3 = 6, v2.v2 = 2, v2.v3 = 5 and v3.v3 = 29.

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Best answer

Thre vectors v1, v2, v3 involve 9 unknown quantities. Since, we are given six equations involving 9 unknown quantities, it is not possible to have uniquely 3 vectors-satisfying these conditions.

As v1.v2 = 4, let us consider v1 = 2k.

Thus, one possible set of vectors is

v1 = 2k, v2 = i + 2k, v3 = – 2i + 4j + 3k.

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