1. Tardigrade
  2. Question
  3. Mathematics
  4. Given that A (3,2,-4), B (5,4-6) and C (9,8,-10) are collinear. Ratio in which B divides AC is 1: m. The value of m is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Given that $A (3,2,-4), B (5,4-6)$ and $C (9,8,-10)$ are collinear. Ratio in which $B$ divides $AC$ is $1: m$. The value of $m$ is

Introduction to Three Dimensional Geometry

Solution:

Suppose B divides $AC$ in the ratio $\lambda: 1$.
$\therefore B=\left(\frac{9 \lambda+3}{\lambda+1}, \frac{8 \lambda+2}{\lambda+1},\frac{-10 \lambda-4}{\lambda+1}\right)=(5,4,-6)$
$\Rightarrow \frac{9 \lambda+3}{\lambda+1}=5,\,\frac{8 \lambda+2}{\lambda+1}=4,\,\frac{-10 \lambda-4}{\lambda+1}=-6$
$\Rightarrow \lambda=\frac{1}{2}$
So, required ratio is $1: 2$.