If `|veca|=5, |vecb|=3, |vecc|=4` and `veca` is perpendicular to `vecb` and `vecc` such that angle between `vecb` and `vecc` is `(5pi)/6`, then the volume of the parallelopiped having `veca, vecb` and `vecc` as three coterminous edges is

Options

A. 30 cubit units
B. 60 cubic units
C. 20 cubic units
D. none of these

Answer

A

Explanation

Since `veca` is perpendicular to both `vecb` and `vecc`. Therefore `veca` is paralel to `vecbxxvecc`.
Now,
`|[(veca,vecb, vecc)]=|veca.(vecbxxvecc)|`
`implies|[(veca, vecb, vecc)]|=|veca||vecbxxvecc| [ :' veca||vecbxxvecc)]`
`implies|[(veca, vecb, vecc]|=|veca||vecb||vecc|"sin"(5pi)/6`
`implies|[(veca, vecb, vecc)]|=5xx3xx4xx1/2=30` cubic units.