Find the ratio in which the line segment joining the points (4,8,10) and (6,10,-8) is divided by the YZ-plane. Options: A . &nbsp internally in the ratio 2:3 B . &nbsp externally in the ratio 2:3 C . &nbsp internally in the ratio 1:2 D . &nbsp externally in the ratio 1:2

Answer: Option B : B Let the YZ-plane divide the line segment joining the points (4,8,10) and (6,10,-8) in the ratio k:1 at the point P. The x-coordinate of the point P is given by x = 4 + 6 k k + 1 Since P lies on the YZ plane, x=0 ⇒ 4 + 6 k = 0 ⇒ k = − 2 3 Hence, the points are divided by the YZ-plane in the ratio 2:3 externally

Find the ratio in which the line segment joining the points (4,8,10) and (6,10

Question

Find the ratio in which the line segment joining the points (4,8,10) and (6,10,-8) is divided by the YZ-plane.

Options:

A . internally in the ratio 2:3

B . externally in the ratio 2:3

C . internally in the ratio 1:2

D . externally in the ratio 1:2

Answer: Option B
:
B

Let the YZ-plane divide the line segment joining the points (4,8,10) and (6,10,-8) in the ratio k:1 at the point P.
The x-coordinate of the point P is given by
$x = \frac{4 + 6 k}{k + 1}$
Since P lies on the YZ plane, x=0
$\Rightarrow 4 + 6 k = 0 \Rightarrow k = \frac{- 2}{3}$