The ratio in which the line joining the points (1, 2, 3) and (-3, 4, -5) is divided by the xy-plane, is

A
$3 : 5$ internally
B
$5 : 3$ externally
C
$3 : 5$ externally
D
$5 : 3$ internally

Solution:

Suppose. the line joining the points $P (1, 2, 3)$ and $Q (- 3, 4, - 5)$ is divided by the xy-plane at a point r is the ratio $λ : 1$ . Then, the coordinates of R are
$(\frac{- 3 λ + 1}{λ + 1}, \frac{4 λ + 2}{λ + 1}, \frac{5 λ + 3}{λ + 1})$

Since R lies on xy-plane i.e., z=0
$∴ \frac{- 5 λ + 3}{λ + 1} = 0 \Rightarrow λ = \frac{3}{5}$
So, the required ratio is $\frac{3}{5} : 1$ or , $3 : 5$ internally

The ratio in which the line joining the points $(1, 2, 3)$ and $(- 3, 4, - 5)$ is divided by the xy-plane, is

Solution:

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