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Let A,B and C be the unit vectors . Sup...

Let A,B and C be the unit vectors . Suppose that A.B=A.C =0 and the angle between B and C is `(pi)/(6)` then prove that `A = +-2(BxxC)`

Text Solution

Verified by Experts

Since `A. B = 0 , A.C = 0`
Hence, `(B+C) A =0`
So, A is perpendicular to` (B+C)`. Further, A is a unit vector perpendicular to the plane of vectors `B` and `C`
`A = +-(BxxC)/(|BxxC|)`
`|BxxC | =|B||C|sin ((pi)/(6)) = 1xx1xx(1)/(2)=(1)/(2)`
`A = +- (BxxC)/(|BxxC|) = +- 2(BxxC)`
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