Consider the problem
Since, required plane is passes through
x−13=y+64=z+12...(1)
So, it passes through point (1,−6,−1)
Since, it is passes through above line (1) and parallel to
x−22=y−13=z+45
So, normal to the plane is perpendicular to vectors
→a=3^i+4^j+2^kand→b=2^i+3^j+5^k
Equation of plane passing through (1,−6,−1) is
A(x−1)+B(y+6)+C(z+1)=0...(1)
since, it is ⊥ to vectors →aand→b
So,
3A+4B+2C=0...(2)2A+3B+5C=0.....(3)
Now, Solving (2) and (3) we get
A20−6=B4−15=C9−8⇒A14=B−11=C1=k
⇒A=14k,B=−11k,C=k
Now putting values of A, B and C in (1) we get,
14k(x−1)+(−11k)(y+6)+k(z+1)=0⇒14(x−1)−11(y+6)+z+1=0⇒14x−14−11y−66+z+1=0⇒14x−11y+z−79=0