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Question

A unit vector perpendicular to the plane determined by the points P(1,-1,2), Q(2,0,-1) and R(0,2,1) is

A
2^i+^j+^k6
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B
2^i+^j+^k3
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C
2^i^j^k3
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D
2^i^j^k3
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Solution

The correct option is A 2^i+^j+^k6
OP=^i^j+2^k,OQ=2^i^k,OR=2^j+^kPQ=OQOP=^i+^j3^k,PR=OROP=^i+3^j^k
PQ×PR=∣ ∣ ∣^i^j^k113131∣ ∣ ∣=8^i+4^j+4^k;|PQ×PR|=64+16+16=96=46
Required unit vectors = ±8^i+4^j+4^k46=±2^i+^j+^k6

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