Find the coordinates of the point which divides the line segment … - Vidyadip

Question

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.

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Answer

Let P (x, y, z) be any point which divides the line segment joining points A(-2, 3, 5) and B(1, -4, 6) in the ratio 2 : 3 externally.
Then
x = $\frac{{2 \times 1 + ( - 3) \times - 2}}{{2 + ( - 3)}} = \frac{{2 + 6}}{{ - 1}} = - 8$
y = $\frac{{2 \times - 4 + ( - 3) \times 3}}{{2 + ( - 3)}} = \frac{{ - 8 - 9}}{{ - 1}} = 17$
z = $\frac{{2 \times 6 + ( - 3) \times 5}}{{2 + ( - 3)}} = \frac{{12 - 15}}{{ - 1}} = 3$
$\therefore$ Coordinates of P are (-8, 17, 3)

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