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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?
  1. x11=y32=z+45
  2. x41=y51=z51
  3. x22=y32=z+33
  4. x+33=4y3=z+12


Solution

The correct option is A x11=y32=z+45
Let x42=y52=z31=λ
x=2λ+4, y=2λ+5, z=λ+3 lies on the plane x+y+z=2
so, 2λ+4+2λ+5+λ+3=2
λ=2
Hence, (x,y,z)(0,1,1)
which is satisfying x11=y32=z+45

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