Question

The equation of the plane containing the two lines of intersection of the two pairs of planes x + 2y – z – 3 = 0 and 3x – y + 2z – 1 = 0, 2x – 2y + 3z = 0 and x – y + z + 1 =0 is :

• A. 7x – 7y + 8z + 3 = 0
• B. 7x – 8y + 9z + 3 = 0
• C. 5x – 5y + 6z + 2 = 0
• D. None of these

Answer 1

The correct option is D None of these

The planes through given lines of intersection are
$(x+2y-z-3)+\lambda (3x-y+2z-1)=0....\left(1\right)$
and $(2x-2y+3z)+\mu (x-y+z+1)=0....\left(2\right)$
Planes (1) and (2) are same. Comparing the coefficients,
we get, $\frac{1+3\lambda }{2+\mu }=\frac{2-\lambda }{-2-\mu }=\frac{-1+2\lambda }{3+\mu }=\frac{-3-\lambda }{\mu }$
Solving for $\lambda ,\mu$, these equations are inconsistent. Therefore, there exists no such plane i.e., the lines are neither parallel nor intersecting.