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If overset(to)(a) , overset(to)(b) " an...

If `overset(to)(a) , overset(to)(b) " and " overset(to)( c)` are unit coplanar vectors then the scalar triple product `[2 overset(to)(a) - overset(to)(b), 2 overset(to)(b) - overset(to)(c ) ,2 overset(to)(c ) - overset(to)(a)]` is

A

0

B

1

C

`-sqrt(3)`

D

`sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
If `vec(a) , vec(b) , vec(c ) ` are coplanar vectors then `2vec(a)-vec(b) ,2vec(b) - vec(c ) ` and `2vec( c) - vec(a) ` are also coplanar vectors.
`I.e., [2vec(a) -vec(b) 2vec(b) -vec(c ) vec(c ) -vec(a)]=0`
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