If the position vectors of the vertices A, B and C are 6i, 6j and k respectively w.r.t origin O, then the volume of the tetrahedron OABC is

Options

A. 6 cu units
B. 3 cu units
C. `1/6` cu units
D. `1/3` cu units

Answer

A

Explanation

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