Question

The direction ratios of two perpendicular lines are $1,-3,5$ and $\lambda ,1+\lambda ,2+\lambda$ Then $\lambda$ is

• A. $-\frac{7}{3}$
• B. $-\frac{7}{2}$
• C. $-\frac{1}{4}$
• D. $-\frac{1}{2}$

Answer 1

The correct option is A $-\frac{7}{3}$

We know that scalor product of two perpendicular vectors is zero.

as $\cos \theta =0$

$a_1{a}_2+b_1{b}_2+c_1{c}_2=0$

$\therefore (1\times \lambda )\left(\right(-3)\times (1+\lambda \left)\right)\left(\right(5)\times (2+\lambda \left)\right)$

$\lambda -3-3\lambda +10+5\lambda =0$

$3\lambda =-7$

$\lambda =\frac{-7}{3}$

Therefore option (A) is Correct.