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If the position vectors of the vertices A, B and C are `6hat(i), 6hat(j)` and `hat(k)` repsectively w.r.t. origin O, the volume of the tetrahedron OABC is

A

6 cu units

B

3 cu units

C

`1/6` cu units

D

`1/3` cu units

Text Solution

Verified by Experts

The correct Answer is:
A
Given that, the position vectors of the vertices A, B and C are
`OA =6 hati =6 hati+0 hatj+0hatk`
`OB=6 hatj =0hati +6 hatj +0hatk`
`and OC =hatk=0hati+0hatj+hatk`
Now, volume of the tetahedron
`=1/6{OA OB OC ]=1/6 |{:(6,0,0),(0,6,0),(0,0,1):}|`
`=1/6(6xx6xx1)=6` cu units
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