Question

An equation of the plane passing through the line of intersection of the planes x + y + z = 6 and 2x + 3y + 4z + 5 = 0 and the point (1, 1, 1) is

• A. 2x + 3y + 4z = 9
• B. x + y + z = 3
• C. x + 2y + 3z = 6
• D. 20x + 23y + 26z = 69

Answer 1

The correct option is D 20x + 23y + 26z = 69

Equation of any plane through the line of intersection of the given planes is
$2x+3y+4z+5+\lambda (x+y+z-6)=0$
It passes through $(1,1,1)if(2+3+4+5)+\lambda (1+1+1-6)=0\Rightarrow \lambda =\frac{14}{3}$ and the required equation is therefore, 20x + 23y + 26z = 69.