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If the vectors ikijk3i^+5k^,4i^+2j^-3k^ and ijk3i^+j^+4k^ are the coterminus edges of the parallelopiped, then find the volume of the parallelopiped. - Mathematics and Statistics

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Sum

If the vectors `3hat"i" + 5hat"k", 4hat"i" + 2hat"j" - 3hat"k"` and `3hat"i" + hat"j" + 4hat"k"`  are the coterminus edges of the parallelopiped, then find the volume of the parallelopiped.

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Solution

Let `bar"a" = 3hat"i" + 5hat"k" , bar"b" = 4hat"i" + 2hat"j" - 3hat"k", bar"c" = 3hat"i" + hat"j" + 4hat"k"`

∴ `[bar"a",bar"b",bar"c"] = |(3,0,5),(4,2,-3),(3,1,4)|`

= 3(8 + 3) - 0(16 + 9) + 5(4 - 6)

= 33 - 0 - 10

= 23

∴ volume of the parallelopiped = `[bar"a",bar"b",bar"c"]`

= 23 cubic units.

Concept: Scalar Triple Product of Vectors
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