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Volume of the parallelopiped having vert...

Volume of the parallelopiped having vertices at ` O-=(0,0,0) , A-=(2,-2,1),B-=(5,-4,4), and C= (1,-2,4)` is

A

5 cu unit

B

10 cu unit

C

15 cu unit

D

20 cu unit

Text Solution

Verified by Experts

The correct Answer is:
B
Given , `vec(OA) = 2 hati- 2 hatj+hatk`
`vec(OB)=5hati-4hatj+4hatk and vec(OC)=hati-2hatj+4hatk`
Volume of parallelopiped`=[vec(OA) vec(OB) vec(OC)]`
`=|{:( 2,-2,1),(5,-4,4),(1,-2,4):}|`
`=2(-16+8)+2(20-4)+1 (-10+4)`
`=10` cu unit
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