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Question

The distance of the point (1,-2,3) from the plane x-y+z=5, measured parallel to the line x2=y3=z6

A
17
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B
1
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C
7
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D
None of these
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Solution

The correct option is B 1
Point is (1,2,3)
Equation of plane = xy+z=5
Equation of parallel line is x2=y3=z6
x12=y+23=z36=λ
x=2λ+1,y=3λ2,z=6λ+3
Since,
xy+z=5
2λ+13λ+26λ+3=5
7λ+6=5
λ=17
Thus,
x=97,y=117,z=157
Therefore,
Distance = (27)2+(37)2+(67)2 = 4949 = 1 unit

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