UPSC NDA Math Model Paper 10

Let XY plane divides the line joining the points A(2, 3, -5) and B(-1, -2, -3) in the ratio k : 1
Using the section formula, the coordinate of the point of intersection is given by
(

−k+2

k+1

,

−2k+3

k+1

,

−3k−5

k+1

)
As we know, on the XY plane z-coordinate is zero.
Therefore,

−3k−5

k+1

=0
⇒−3k−5=0
⇒−3k=5
⇒

k

1

=

−5

3

Therefore, the ratio is 5:3 externally