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Question

Given α=3^i+^j+2^k and β=^i2^j4^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 A 5
AB=βα=2^i3^j6^k

Equation of the plane passing through B and perpendicular to AB is
(rOB).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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