# The point which divides the line joining the points $(2,4,5)\:\:and\:\:(3,5,-4)$ in the ratio $2:3$ externaly lies on the plane?

$(a)\:ZOX\:Plane\:\:\:\qquad\:(b)\:XOY\:Plane\;\;\;\qquad\:(c)\:YOZ\:Plane\:\:\:\qquad\:(d)\:None\:of\:these.$

Toolbox:
• Section formula: The coordinates of the point, that divides $P(x_1,y_1,z_1)\:and\:Q(x_2,y_2,z_2)$ in the ratio $l:m$ externally is given by $\bigg(\large\frac{lx_2-mx_1}{l-m},\:\frac{ly_2-my_1}{l-m},\:\frac{lz_2-mz_1}{l-m}\bigg)$
• If $x\:coordinate$ of any point is zero, then the point lies on $YOZ$ plane.
Let $P(2,4,5)\:\:Q(3,5,-4)$ be the given two points.
From section formula. the point $R(x,y,z)$ that divides $PQ$ in the ratio $2:3$ externally is
given by $R(x,y,z)=\big(\large\frac{6-6}{2-3},\:\frac{10-12}{2-3},\:\frac{-8-15}{2-3}\big)$$=(0,-2,23)$
Since the $x\: coordinate$ of $R$ is $zero$, $R$ lies on $YOZ\:Plane.$