Question

The $xy$ plane divides the line joining the points $(-1,3,4)$and $(2,-5,6)$

• A. internally in the ratio $2:3$
• B. externally in the ratio $2:3$
• C. internally in the ratio $3:2$
• D. externally in the ratio $3:2$

Answer 1

The correct option is B

externally in the ratio $2:3$

Explanation of the correct option.

Let the ratio be $\lambda :1$.

So, $\left(\frac{2\lambda -1}{\lambda +1},\frac{-5\lambda +1}{\lambda +1},\frac{6\lambda +4}{\lambda +1}\right)$ lies on $xy$ plane.

Given : It is in the $xy$ plane.

Thus, $z=0$. (The $z$-axis component)

$\frac{6\lambda +4}{\lambda +1}=0$

$\Rightarrow$ $\lambda =-\frac{4}{6}$

$\Rightarrow$ $\lambda =-\frac{2}{3}$

Since the value of $\lambda$ is negative, it divides externally in the ratio $2:3$.

Hence, option B is the correct option.