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Question
Find the volume of the parallelepiped whose coterminous edges are represented by the vectors `- 6hat"i" + 14hat"j" + 10hat"k", 14hat"i" - 10hat"j" - 6hat"k"` and `2hat"i" + 4hat"j" - 2hat"k"`
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Solution
Volume of the parallelepiped = `[bar"a", bar"b", bar"c"]`
= `|(-6, 14, 10),(14, -10, -6),(2, 4, -2)|`
= – 6(20 + 24) – 14(– 28 + 12) + 10(56 + 20)
= – 6(44) – 14(– 16) + 10(76)
= – 264 + 224 + 760
= 720 cu.units
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