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Question

The distance of the point (1,2,3) from the plane xy+z=5 measured parallel to a line, whose direction ratios are 2,3,6 is

A
2
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B
5
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C
3
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D
1
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Solution

The correct option is D 1
Equation of line through point (1,2,3) and parallel
to line with direction ratios 2,3,6 is
L:x12=y+23=z36=λ (say)
Any point on line L is P(2λ+1,3λ2,6λ+3)
Since P lies on plane, xy+z=5
2λ+13λ+26λ+3=5
λ=17
Required distance
=(2λ)2+(3λ)2+(6λ)2
=7λ
=1 unit

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