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Question
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.
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.
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