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If a is perpendicular to b and c, |a|=2,...

If a is perpendicular to b and c, `|a|=2, |b|=3`, `|c|=4` and the angle between b and c is `(2pi)/3`, then `[(a, b, c)]` is equal to

A

`4sqrt(3)`

B

`6sqrt(3)`

C

`12sqrt(3)`

D

`18sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
`[abc]=a*(bxxc)=a*(|b||c|sin(2pi)/3hatn)`
` =|b||c| sin (2pi)/(3)A(.hatn)`
`=|b||c|sin""(2pi)/3|a||hatn|cos60^@`
`=|a||b||c|(sin(2pi)/3)`
`2xx3xx4xxsqrt3/2=12sqrt3`
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