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Let vec(x), vec(y) and vec(z) be three v...

Let `vec(x), vec(y) and vec(z)` be three vectors each of magnitude `sqrt2` and the angle between each pair of them is `(pi)/(3)`. If `vec(a)` is a non-zero vector perpendicular to `vec(x) and vec(y) xx vec(z) and vec(b)` is a non-zero vector perpendicular to `vec(y) and vec(z) xx vec(x)`, then

A

`vec(b) = (vec(b).vec(z)) (vec(z) - vec(x))`

B

`vec(a) = (vec(a).vec(y)) (vec(y) - vec(z))`

C

`vec(a).vec(b) = - (vec(a).vec(y)) (vec(b).vec(z))`

D

`vec(a) = (vec(a).vec(y)) (vec(z) - vec(y))`

Text Solution

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The correct Answer is:
A, B, C
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