The ratio in which the plane $2 x + 3 y - 2 z + 7 = 0$ divides the line segment joining the points $(- 1, 1, 3)$ , $(2, 3, 5)$ is

3 : 5

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7 : 5

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9 : 11

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1 : 5

externally

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Solution

The correct option is D $1 : 5$ externally
Let the plane divide the line $A B$ at $C$ in the ratio $k : 1$
The coordinayes of $C$ $= (\frac{2 k - 1}{k + 1}, \frac{3 k + 1}{k + 1}, \frac{5 k + 3}{k + 1})$
Since this point lies on the plane $2 x + 3 y - 2 z + 7 = 0$
Therefore
$2 (\frac{2 k - 1}{k + 1}) + 3 (\frac{3 k + 1}{k + 1}) - 2 (\frac{5 k + 3}{k + 1}) + 7 = 0$
$\Rightarrow 4 k - 2 + 9 k + 3 - 10 k - 6 + 7 k + 7 = 0$
$\Rightarrow 10 k + 2 = 0$
$\Rightarrow k = \frac{- 2}{10} = \frac{- 1}{5}$
If the divides the line in the ratio $1 : 5$ externally

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Similar questions

Ratio in which line $2 x + 3 y - 5 = 0$ divides the line segment joining the points A(8 , -9) and B(2 , 1) is .

2 x + 3 y + 5 z = 1

(1, 0, - 3)

(1, - 5, 7)

A (4, - 2, 5)

(- 2, 3, 7)

8 : 5

Which of the following statments are correct?

1. The coordinates of the point which divides the line segment joining the points

$(1, - 2, 3)$ and $(3, 4, - 5)$ internally in the ratio $2 : 3$ is $(- 3, - 14, 19)$ .

2. The coordinates of the point which divides the line segment joining the points

$(1, - 2, 3)$ and $(3, 4, - 5)$ externally in the ratio $2 : 3$ is $(\frac{9}{5}, \frac{2}{5}, \frac{- 1}{5})$ .

(- 3, - 4)

(- 8, 7)

7 : 5

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