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in 3D Coordinate Geometry by (50.8k points)
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Find the ratio in which the point C(5, 9, -14) divides the join of A(2, -3, 4) and B(3, 1, -2).

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Given: Point A(2, -3, 4) and B(3, 1, -2) divided by a point C(5, 9, -14)

Let the ratio be k:1 in which point C divides point A and point B.

We know below are the coordinates of a point which divides a line segment in ratio, k:1.

Using section formula, We have

Find the value of k:

Choosing first co-ordinate,

5 = (3k+2)/(k+1)

5k + 5 = 3k + 2

2k = -3

Or k = -3/2

Since, the ratio is -3:2, division is external. Therefore, external division ratio is 3:2.

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