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Question
A unit vector perpendicular to the plane passing through the points whose position vectors are ^i−^j+2^k, 2^i−^k and 2^j+^k is
A unit vector perpendicular to the plane passing through the points whose position vectors are ^i−^j+2^k, 2^i−^k and 2^j+^k is
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Solution
The correct option is D None of these
Two directions of line segments joining the above given three points are ^i−^j−3^k and 2^i−2^j−2^k.
The normal to the plane will be their cross product, thereby giving (^i−^j−3^k)×(2^i−2^j−2^k)=−2^k+2^j+2^k+2^i−6^j−6^i=−4^i−4^j
Unit vector is 1√2(^i+^j)
Two directions of line segments joining the above given three points are ^i−^j−3^k and 2^i−2^j−2^k.
The normal to the plane will be their cross product, thereby giving (^i−^j−3^k)×(2^i−2^j−2^k)
=−2^k+2^j+2^k+2^i−6^j−6^i
=−4^i−4^j
Unit vector is 1√2(^i+^j)
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