Find the coordinates of the point which divides the line segment joining the points (- 2, 3, 5) and (1, – 4,6) in the ratio 2 : 3 externally.

# Find the coordinates of the point which divides the line segment joining the points (- 2, 3, 5) and (1, - 4,6) in the ratio 2 : 3 externally.

1. A

(- 8, - 17, 3)

2. B

(- 8, 17, 3)

3. C

(8, - 17, 3)

4. D

None of the above

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### Solution:

Let the point C divides the line externally in the ratio 2:3.

Here, the ratio is 2 :3.
m=2,n=3
The coordinates of point C

$\begin{array}{l}=\left[\left(\frac{{\mathrm{mx}}_{2}-{\mathrm{nx}}_{1}}{\mathrm{m}-\mathrm{n}}\right),\left(\frac{{\mathrm{my}}_{2}-{\mathrm{ny}}_{1}}{\mathrm{m}-\mathrm{n}}\right),\left(\frac{{\mathrm{mz}}_{2}-{\mathrm{nz}}_{1}}{\mathrm{m}-\mathrm{n}}\right)\right]\\ ⇒\mathrm{C}=\left[\frac{2×\left(1\right)-3×\left(-2\right)}{\left(2-3\right)},\frac{2×\left(-4\right)-3×3}{\left(2-3\right)},\frac{2×6-3×5}{\left(2-3\right)}\right]\\ =\left[\frac{2+6}{\left(-1\right)},\frac{-8-9}{\left(-1\right)},\frac{12-15}{\left(-1\right)}\right]=\left(-8,17,3\right)\end{array}$  Register to Get Free Mock Test and Study Material

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