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
Answer: Option A
:
A
−−→OP=^i−^j+2^k,−−→OQ=2^i−^k,−−→OR=2^j+^k⇒−−→PQ=−−→OQ−−−→OP=^i+^j−3^k,−−→PR=−−→OR−−−→OP=−^i+3^j−^k
−−→PQ×−−→PR=∣∣
∣
∣∣^i^j^k11−3−13−1∣∣
∣
∣∣=8^i+4^j+4^k;|−−→PQ×−−→PR|=√64+16+16=√96=4√6
Required unit vectors = ±8^i+4^j+4^k4√6=±2^i+^j+^k√6
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:
A
−−→OP=^i−^j+2^k,−−→OQ=2^i−^k,−−→OR=2^j+^k⇒−−→PQ=−−→OQ−−−→OP=^i+^j−3^k,−−→PR=−−→OR−−−→OP=−^i+3^j−^k
−−→PQ×−−→PR=∣∣
∣
∣∣^i^j^k11−3−13−1∣∣
∣
∣∣=8^i+4^j+4^k;|−−→PQ×−−→PR|=√64+16+16=√96=4√6
Required unit vectors = ±8^i+4^j+4^k4√6=±2^i+^j+^k√6
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