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Question

The distance of the point (1, -5, 9) from the plane x - y + z = 5 measured along the line x = y = z is


A

310

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B

103

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C

103

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D

203

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Solution

The correct option is B

103


Equation of line passing through the point (1, -5, 9) and parallel to x = y = z is
x11=y+51=z91=λ
Thus, any point on this line is of the form
λ+1,λ5,λ+9.
Now, if P(λ+1,λ5,λ+9) is the point of intersection of line and plane, then
(λ+1)(λ5)+λ+9=5
λ+15=5λ=10
Coordintes of point P are (-9, -15, -1).
Hence, required distance
=(1+9)2+(5+15)2+(9+1)2
=102+102+102=103


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