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Question

# Let P,Q,R be points with position vectors →r1=3^i−2^j−^k,→r2=^i+3^j+4^k and →r3=2^i+^j−2^k relative to an origin O. The distance of P from the plane OQR is

A
2
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B
3
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C
1
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D
113
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Solution

## The correct option is B 3Let P,Q,R be points with the given position vectorsEquation of the plane OQR is r =λ→r2+μ→r3,i.e. →r⋅(→r2×→r3)=0So, the distance of P from the plane OQR is ∣∣∣→r1.(→r2×→r3)|→r2×→r3|∣∣∣.Since, →r2×→r3=−10^i+10^j−5^k, so |→r2×→r3|=15And the perpendicular distance =∣∣∣−30−20+515∣∣∣=3Hence, option B is correct.

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