If the lines $\frac{x-1}{-3}=\frac{y-2}{2\lambda }=\frac{z-3}{2}$ and $\frac{x-1}{3\lambda }=\frac{y-1}{2}=\frac{z-6}{-5}$ are perpendicular. Then the value of $\lambda $ is :

-2

The correct answer is Option (2) → -2

$\vec{v_1}$ || line 1: = $-3\hat i+2λ\hat j+2\hat k$

$\vec{v_2}$ || line 2: = $3λ\hat i+2\hat j-5\hat k$

as $\vec{v_1}.\vec{v_2}=0⇒-9λ+4λ-10=0$

so $5λ=-10$

$⇒λ=-2$