The number of distinct real values of `lamda` for which the lines `(x-1)/(1) = (y-2)/(2) = (z+3)/(lamda ^(2)) and (x-3)/(1) = (z-1)/(2)` are coplanar is :

Options

A. 3
B. 2
C. 1
D. 4

Answer

A

Explanation

Given lines will be coplanar if
`|(1-3,2-2,-3-1),(1,2,lamda^(2)),(1,lamda^(2),2)|=0`
`implies|(-2,0,-4),(1,2,lamda^(2)),(1,lamda^(2),2)|=0`
`implies-2(4-lamda^(4))-4(lamda^(2)-2)=0`
`implieslamda^(4)-2lamda^(2)=0implieslamda=0,+-sqrt(2)`
Hence there are three values of `lamda`.