Mathematics

Problem

Consider the lines

L_1: \frac{x-1}{2} = \frac{y}{-1} = \frac{z+3}{1}

L_2: \frac{x-4}{1} = \frac{y+3}{1} = \frac{z+3}{2}

and the planes

P_1: 7x + y + 2z = 3, P_2: 3x + 5y - 6z = 4

. Let

ax + by + cz = d

the equation of the plane passing through the point of intersection of lines

L_1

and

L_2

and perpendicular to planes

P_1

and

P_2

. Match List I with List II and select the correct answer using the code given below the lists.

a. P-3 Q-2 R-4 S-1 b. P-1 Q-3 R-4 S-2 c. P-3 Q-2 R-1 S-4 d. P-2 Q-4 R-1 S-3