Write the value of λ for which the lines (x - 3)/-3 = (y + 2)/2λ = (z + 4)/2

Question

Write the value of λ for which the lines \(\frac{x-3}{-3}=\frac{y+2}{2\lambda}=\frac{z+4}{2}\) and \(\frac{x+1}{3\lambda}=\frac{y-2}{1}=\frac{z+6}{-5}\) are perpendicular to each other.

Answer 1

We have,

The given lines are parallel to vectors,

Now, for \(\vec {b_1} \perp \vec {b_2}\) we must have,