We know that, the equation of a plane through the line of intersection of the planes
So, equation of the plane passing through the line of intersection of the plane
We know that two planes perpendicular if
\(\vec n_1.\vec n_2=0\)
Given that plane (1) is perpendicular to the plane
Using (1)and (3) in equation (2),
(1 + 2k)(5) + (2 + k)(3) + (3 – k)( – 6) = 0
5 + 10k + 6 + 3k – 18 + 6k = 0
19k – 7 = 0
k = \(\cfrac{7}{19}\)
Put the value of k in equation (1),
Multiplying by 19,
33x + 45y + 50z – 41 = 0
