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Question
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
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
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Solution
The correct option is A 5
−−→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.
−−→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.
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