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If the position vectors of the vertic...

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

A

` 6 `

B

` 3 `

C

` ( 1 )/( 6 ) `

D

` (1 )/( 3 ) `

Text Solution

Verified by Experts

The correct Answer is:
A
Given that, the position vectors of the vertices A, B and C are
`OA = 6i= 6i+0j+0k `
OB =6j=0i+6j+0k
OC = k=0i+0j +k
Now, volume of the tetrahedron
` = ( 1 )/ ( 6 ) ` [OA OB OC]
= ` ( 1 ) / ( 6 ) |{:( 6,,0,,0),(0,,6,,0), ( 0,,0,,1):}| `
= ` ( 1 ) / ( 6 ) ( 6 xx 6 xx 1 ) = 6 `
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