Question

A line is drawn from the point P(1,1,1) and perpendicular to a line with direction ratios (1,1,1) to intersect the plane x+2y+3z=4 at Q The locus of point Q is

• A. $\frac{x}{1}=\frac{y-5}{-2}=\frac{z+2}{1}$
• B. $\frac{x}{-2}=\frac{y-5}{1}=\frac{z+2}{1}$
• C. $x=y=z$
• D. $\frac{x}{2}=\frac{y}{3}=\frac{z}{5}$

Answer 1

The correct option is A $\frac{x}{1}=\frac{y-5}{-2}=\frac{z+2}{1}$

Through P we can draw infinite lines perpendicular to a line with d.r's $(1,1,1)$ which all lie on a plane.
So Locus of 'Q' is the line of intersection of the plane x + 2y + 3z = 4 and the plane
1(x+1) + 1(y-1)+1(z-1) = 0 $\Rightarrow$ then the line is $\frac{x}{1}=\frac{y-5}{-2}=\frac{z+2}{1}$