Question

The values of $a$ for which point $(8,-7,a),(5,2,4)$ and $(6,-1,2)$ are collinear.

• A. $-4$
• B. $-2$
• C. $0$
• D. $2$

Answer 1

The correct option is B $-2$

Let the points be $A(8,-7,a),B(5,2,4),C(6,-1,2)$
Direction ratio of $BC=(1,-3,-2)$
If $A,B,C$ are collinear points then direction ratio of $BC$ and $AB$ must be proportional.
Direction ratio of $AB=(-3,9.4-a)$
$\therefore -3=\lambda 1$
$\therefore 9=\lambda (-3)$
$\therefore 4-a=\lambda (-2)$ and $\lambda =-3$
$\therefore \frac{4-a}{-3}=-2$

$\therefore a=-2$