Find the coordinates of a point which divides the line segment joining the points (5, 4, 2) and (-1, -2, 4) in the ratio

(i) 2 :3 internally.

(ii) 2 :3 externally.

Or

Find the points on Z-axis which are at a distance $\sqrt{21}$ from the point (1, 2,3).

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Solution

(i) $(\frac{13}{5}, \frac{8}{5}, \frac{14}{5})$ (ii) (17, 16, -2)

Or

(i) (0, 0, -1), (0, 0, 7)

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Similar questions

Which of the following statments are correct?

1. The coordinates of the point which divides the line segment joining the points

$(1, - 2, 3)$ and $(3, 4, - 5)$ internally in the ratio $2 : 3$ is $(- 3, - 14, 19)$ .

2. The coordinates of the point which divides the line segment joining the points

$(1, - 2, 3)$ and $(3, 4, - 5)$ externally in the ratio $2 : 3$ is $(\frac{9}{5}, \frac{2}{5}, \frac{- 1}{5})$ .

\frac{x + 1}{2} = \frac{y + 2}{3} = \frac{z - 3}{6}

3

(1, - 2, 3)

(9, 18)

(1, 2)

3 : 6

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