Question

If the points A(9, 8, -10), B(3, 2, -4) and C(5, 4, -6) be collinear, then the point C divides the line AB in the ratio

• A. 2 : 1
• B. 3 : 1
• C. 1 : 2
• D. –1 : 2

Answer 1

The correct option is A

2 : 1

Let point C divides the line AB in the ratio 1 : $\lambda$.
$\therefore 5=\frac{9\lambda +3}{\lambda +1}\Rightarrow 4\lambda =2\Rightarrow \lambda =\frac{1}{2}$
Hence required ratio is 2 : 1.