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

(i) The coordinates of point R that divides the line segment joining points P (*x*_{1}, *y*_{1}, *z*_{1}) and Q (*x*_{2}, *y*_{2}, *z*_{2}) internally in the ratio *m*: *n *are

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Let R (*x*,* y*, *z*) be the point that divides the line segment joining points(–2, 3, 5) and (1, –4, 6) internally in the ratio 2:3

Thus, the coordinates of the required point are.

(ii) The coordinates of point R that divides the line segment joining points P (*x*_{1}, *y*_{1}, *z*_{1}) and Q (*x*_{2}, *y*_{2}, *z*_{2}) externally in the ratio *m*: *n *are

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Let R (*x*,* y*, *z*) be the point that divides the line segment joining points(–2, 3, 5) and (1, –4, 6) externally in the ratio 2:3

Thus, the coordinates of the required point are (–8, 17, 3).

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