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If a=2hati-3hatj+4hatk, b=3hati-4hatj+5h...

If `a=2hati-3hatj+4hatk, b=3hati-4hatj+5hatk` and `c=5hati-3hatj-2hatk` then the volume of the parallelopiped with coterminous edges `a+b,b+c,c+a` is

A

`14`

B

16

C

63

D

8

Text Solution

Verified by Experts

The correct Answer is:
B
Given that `a=2hati-3hatj+5hatk`
`b=3hati-4hatj+5hatk`
and `c=5hati-3hatj-2hatk`
`:.` Volume of parallelopiped where sides are
`a+b,b+c` and `c+a` is
`2 a b c=(2)|(2,-3,5),(3,-4,5),(5,-3,-2)|`
`=(2)[(8+15)+3(-6-25)+5(-9+20)]`
`=2(46-93-55)=16`
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