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Question

On which of the following lines lies the point of intersection of the line, x42=y52=z31 and the plane, x+y+z=2?

A
x22=y32=z+33
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B
x41=y51=z51
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C
x11=y32=z+45
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D
x+33=4y3=z+12
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Solution

The correct option is C x11=y32=z+45
General point on the given line is

x=2λ+4
y=2λ+5
z=λ+3

Solving with plane,

2λ+4+2λ+5+λ+3=2
5λ+12=2
5λ=10
λ=2

x=2×2+4=0
y=2×2+5=1
z=1×2+3=1

Points will satisfy option C

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