Question

The projection of line $3x-y+2z-1=0=x+2y-z-2$ on the plane $3x+2y+z=0$ is

• A. $\frac{x+1}{11}=\frac{y-1}{-9}=\frac{z-1}{-15}$
  
• B. $3x-8y+7z+4=0=3x+2y+z$
  
• C. $\frac{x+12}{11}=\frac{y+8}{-9}=\frac{z+14}{15}$
  
• D. $\frac{x+12}{11}=\frac{y+8}{-9}=\frac{z+14}{-15}$

Answer 1

Answer: (A), (B)

The correct options are
A $\frac{x+1}{11}=\frac{y-1}{-9}=\frac{z-1}{-15}$

B $3x-8y+7z+4=0=3x+2y+z$


Equation of a plane passing through the line $3x-y+2z-1=0=x+2y-z-2$ is
$3x-y+2z-1+\lambda (x+2y-z-2)=0$
Since it is perpendicular to the given plane
$\therefore \lambda =-\frac{3}{2}$
$\therefore$ Equation of the line of projection is
$3x-8y+7z+4=0=3x+2y+z$
Its direction ratios are < 11,-9,-15 > and the point ( -1,1,1) lies on the line
$\therefore \frac{x+1}{11}=\frac{y-1}{-9}=\frac{z-1}{-15}$ is also the equation of the line of projection.