Question

If the points $(-1,3,2),(-4,2,-2)$ and $(5,5,\lambda )$ are collinear, then $\lambda$ is equal to

• A. $-10$
• B. $5$
• C. $-5$
• D. $10$

Answer 1

The correct option is D $10$

Let the points be $A(-1,3,2)B(-4,2,-2)C(5,5,\lambda )$
Direction ratio of $AB=(-3,-1,-4)$
If $A,B,C$ are collinear points then direction ratio of $AB$ and $BC$ must be proportional.
Direction ratio of $BC=(9,3,\lambda +2)$
$\therefore 9=\alpha (-3)$
$\therefore 3=\alpha (-1)$
$\therefore \lambda +2=\alpha (-4)$ and $\alpha =-3$
$\therefore \frac{\lambda +2}{-3}=-4$
$\therefore \lambda =10$