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 $2:1$

REF.Image

Let the ratio be K:1

Then, using section formula

we have

$C(5,4,-6)=\frac{K(3,2,-4)+(9,8,-10)}{K+1}$

$\Rightarrow 5=\frac{3K+9}{K+1}$

$\Rightarrow 5K=3K+4$

$\Rightarrow 2K=4$

$K=2$

$\Rightarrow$ C divides AB in ratio 2:1