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Let vec(a), vec(b), vec(c) be three vect...

Let `vec(a), vec(b), vec(c)` be three vectors mutually perpendicular to each other and have same magnitude. If a vector `vec(r)` satisfies
`vec(a) xx {(vec(r) - vec(b)) xx vec(a)} + vec(b) xx {(vec(r) - vec(c)) xx vec(b)} + vec(c) xx {(vec(r) - vec(a)) xx vec(c)} = vec(0)`, then `vec(r)` is equal to :

A

`(1)/(3) (vec(a) +vec(b)+vec(c))`

B

`(1)/(3) (2 vec(a) + vec(b) - vec(c))`

C

`(1)/(2) (vec(a) + vec(b) +vec(c))`

D

`(1)/(2) (vec(a) +vec(b) + 2vec(c))`

Text Solution

Verified by Experts

The correct Answer is:
C
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