KVPY Sample Paper KVPY Stream-SX Model Paper-31

If a plane passes through intersection of planes \[2x-y-4=0\] and \[y+2z-4=0\] also passes through the point \[(1,1,0).\] Then the equation of plane

A) \[x-y-z=0\]

B) \[2x-z=0\]

C) \[x+2z-1=0\]

D) \[x-z-1=0\]

Correct Answer: A

Solution :

\[{{P}_{1}}+\lambda {{P}_{2}}=0\]

\[(2x-y-4)+\lambda (y+2z-4)=0\]

It passes through (1, 1, 0)\[\Rightarrow \]\[1+\lambda =0\]\[\Rightarrow \] \[\lambda =-1\]

equation of plane is \[x-y-z=0.\]