If P (3, 2, −4), Q (5, 4, −6) and R (9, 8, −10) are collinear, then R divides PQ in the ratio

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3: 2 externally \text{ Suppose the point R divides PQ in the ratio } \lambda: 1 . \text{ Coordinates of R are } \left( 5\lambda + 3/\lambda + 1, 4\lambda + 2/\lambda + 1, - 6\lambda - 4/\lambda + 1 \right) . \text { But the coordinates of R are } \left( 9, 8, - 10 \right) . \therefore 5\lambda + 3/\lambda + 1 = 9, 4\lambda + 2/\lambda + 1 = 8 \text{ and } - 6\lambda - 4/\lambda + 1 = - 10 \text{ From each of these equations, we get } \lambda = - $\frac{3}{2}$ \therefore \text{ R divides PQ in the ratio 3: 2 externally } .

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