1.

Find the volume of the parallelopiped, if the coterminus edges are given by the vectors ` 2hati + 5hatj - 4hatk . 5hati + 7hatj + 5hatk , 4hati + 5hatj - 2hatk`

Answer» Let ` baca = 2hati + 5hatj - 4hatk , barb = 5hati + 7hatj + 5hatk`
` barc = 4hati + 5hatj - 2hatk `
`therefore bara . (baraxxbarc) = |{:(2,5,-4),(5,7,5),(4,5,-2):}|`
` = 2(-14 - 25 ) - 5 (- 10 - 20 ) - 4 (25 - 28) `
` = - 78 + 150 + 12 = 84 `
` therefore ` Volume of parallelopiped is 84 cubic units.


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