If the equation of plane containing lines $\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-1}{3}$and  $\frac{x-3}{-4}=\frac{z-2}{2}=\frac{z-1}{-6}$is  $9x+by+cz=d$ then $\left(b+c+d\right)$  is

detailed solution

Correct option is C

The equation of the plane containing two parallel lines  x−x1a1=y−y1b1=z−z1c1and  x−x2a1=y−y2b1=z−z2c1is x−x1y−y1z−z1x2-x1y2−y1z2−z1a1b1c1=0The given two lines are parallel, because their direction ratios are proportional with2,−1,3Hence, the equation of the plane containing the both lines is x−1y+1z−13−12+11−12−13=0Simplifying  x−19−y+16+z−1−2−6=09x−9−6y−6−8z+8=09x−6y−8z−7=09x−6y−8z=7      Compare this equation with  ax+by+cz=dHence,b+c+d=−6−8+7=−7