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Question

The vector equation of a plane which is at a distance of 9 units from the origin and which is normal to the
vector 2ˆiˆj+2ˆk is

A
r.(2ˆiˆj+2ˆk)=27
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B
r.(2ˆiˆj+2ˆk)=9
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C
r.(2ˆiˆj+2ˆk)=3
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Solution

The correct option is A r.(2ˆiˆj+2ˆk)=27
The vector equation of a plane is given in the form r.ˆn=d
Here d = 9 and

ˆn=2ˆiˆj+2ˆk22+(1)2+22=23ˆi13ˆj+23ˆk
So,
r. (23ˆi13ˆj+23ˆk) = 9
r . (2ˆiˆj+2ˆk) =27.

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