Question

If the direction cosines of the line common to the planes \[ x+2y-z-1=0 \] and \[ 3x-4y+z-5=0 \] are \((l,m,n)\), then \(|l+m-n|=\)

• A. \(\frac6{\sqrt{30}}\)
• B. \(\frac4{\sqrt{30}}\)
• C. \(\frac2{\sqrt{30}}\)
• D. \(\frac8{\sqrt{30}}\)

Hint:

The line of intersection of two planes is perpendicular to both normals, so its direction vector is their cross product.

Answer 1

The Correct Option is C