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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 units

B

10 cu units

C

15 cu units

D

20 cu units

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `OA=2 hati-2hatj+hatk`
`OB=5hati-4hatj+4hatk` and `OC=hati-2hatj+4hatk`
Volume of parallelopiped`=["OA OB OC"]`
`=|{:(2,-2,1),(5,-4,4),(1,-2,4):}|=2(-16+8)+2(20-4)+1(-10+4)`
`=-16+32-6=10` cu units.
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