Since, we know that the equation of plane passing through a point (x1,y1,z1) is A(x−x1)+B(y−y1)+C(z−z1)=0 Equation of plane passing through (0,1,2) is A(x−0)+B(y−1)+C(z−2)=0 ...(i) ∵ Plane (i) passes through (−1,0,3). Hence, A(−1−0)+B(0−1)+C(3−2)=0 ⇒−A−B+C=0 ⇒A+B−C=0 ...(ii) If plane (i) is perpendicular to 2x+3y+z=5 ∴2A+3B+C=0 [by using condition of perpendicularly] On solving Eqs. (ii) and (iii),
A
1.1−3(−1)
=
B
2(−1)−1.1
=
C
1.3−2.1
⇒
A
4
=
B
−3
=
C
1
Using these proportional values of A,B,C in Eq. (i), 4(x−0)+(−3)(y−1)+(z−2)=0 ⇒4x−3y+z+1=0