Question

If the points $(0,2,5),(1,-2,4),(2,a,3)$ are collinear then which of the following is/are correct ?

• A. $a=-6$
• B. $a=6$
• C. $a^2-5a-6=0$
• D. $a^2+5a-6=0$

Answer 1

Answer: (A), (D)

$a^2+5a-6=0$

For collinear points:
$\Rightarrow \frac{x_3-x_1}{x_2-x_1}=\frac{y_3-y_1}{y_2-y_1}=\frac{z_3-z_1}{z_2-z_1}$
$\Rightarrow \frac{2-0}{1-0}=\frac{a-2}{-2-2}=\frac{3-5}{4-5}$
$\Rightarrow \frac{a-2}{-4}=2$
$\Rightarrow a=-6$