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Let `overset(to)(a),overset(to)(b),overset(to)(c )` be unit vectors such that `overset(to)(a)+overset(to)(b)+overset(to)(c ) = overset(to)(0).`
Which one of the following is correct ?

A

`overset(to)(a)xxoverset(to)(b)=overset(to)(b)xxoverset(to)(c)=overset(to)(c)xxoverset(to)(a)=overset(to)(0)`

B

`overset(to)(a)xxoverset(to)(b)=overset(to)(b)xxoverset(to)(c)=overset(to)(c)xxoverset(to)(a)neoverset(to)(0)`

C

`overset(to)(b)xxoverset(to)(b)=overset(to)(b) xx overset(to)(c) =overset(to)(a)xxoverset(to)(c)=overset(to)(0)`

D

`overset(to)(a)xxoverset(to)(b),overset(to)(b)xxoverset(to)(c),overset(to)(c)xxoverset(to)(a)` are mutually perpendicular

Text Solution

Verified by Experts

The correct Answer is:
B
Since `vec(a) ,vec(b) , vec( c) ` are unit vectors and `vec(a) + vec(b) + vec( c) =vec(0)` then `vec(a) , vec(b) , vec( c) ` represent and aquilateral triangle .
`:. , vec(a) xx vec(b) = vec(b) xx vec(c ) = vec(c ) xx vec(a) be vec(0) `
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