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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

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`since ,A.B=O A.C=O`
` Hence , (B+C).A=O`
so ,A is perpendicular to (B+C)and A is a unit vector perpendicular to the polane of vector BandC.
`A=(BxxC)/(|BxxC|)`
`where ,|BxxC|=|B||C|sintheta`
` =|B||c|"sin"(pi)/(6) (therefore sintheta=(pi)/(6))`
`=1xx1xx(1)/(2)=(1)/(2)`
`A=(BxxC)/(|BxxC|)=+-2(BxxC)`
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