Question

The ratio in which the join of $(1,-2,4)$ and $(4,2,-1)$ divided by the $X-Y$ plane is

• A. $1:3$
• B. $3:1$
• C. $4:1$
• D. $1:4$

Answer 1

The correct option is C $4:1$

Let $P$ be the point where the line joining the given two points $(1,-2,4)$ and $(4,2,-1)$ intersects the $X-Y$ plane in $m:n$ ratio. We are to find $m:n$.

Now the co-ordinate of the point $P$ be $(\frac{4m+n}{m+n},\frac{2m-2n}{m+n},\frac{-m+4n}{m+n})$.

As the point $P$ lies on the $X-Y$ plane,

$\frac{-m+4n}{m+n}=0$

or, $-m+4n=0$

or, $\frac{m}{n}=\frac{4}{1}$

or, $m:n=4:1$