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Question

If ¯a is unit vector, then |¯a×^i|2+|¯a×^j|2+|¯a×^k|2= _____________.

A
2
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B
1
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C
0
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D
3
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Solution

The correct option is A 2
Let x,y and z be the direction angles of the vector a
Then,
|a׈i|=|a||ˆi|sin(x)=sinx
Similarly,
|a׈j|=siny
|a׈k|=sinz

Therefore, |a׈i|2+|a׈j|2+|a׈k|2=sin2x+sin2y+sin2z
=(1cos2x)+(1cos2y)+(1cos2z)
=3(cos2x+cos2y+cos2z)
=31
=2

Hence, the answer is option (A).

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