Given →α=3^i+^j+2^k and →β=^i−2^j−4^k are the position vectors of the points A and B. Then the distance of the point −^i+^j+^k from the plane passing through B and perpendicular to AB is
A
5
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B
10
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C
15
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D
20
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Solution
The correct option is A5 −−→AB=→β−→α=−2^i−3^j−6^k
Equation of the plane passing through B and perpendicular to AB is (→r−−−→OB).−−→AB=0 →r.(2^i+3^j+6^k)+28=0
Hence, the required distance from is =∣∣
∣∣(−^i+^j+^k).(2^i+3^j+6^k)+28|2^i+3^j+6^k|∣∣
∣∣ =∣∣∣−2+3+6+287∣∣∣ =5 units.