The point which divides the line joining the points $(1, 3, 4)$ and $(4, 3, 1)$ internally in the ratio $2 : 1,$ is

(2, - 3, 3)

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(2, 3, 3)

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(\frac{5}{2}, 3, \frac{5}{2})

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(- 3, 3, 2)

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(3, 3, 2)

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Solution

The correct option is E $(3, 3, 2)$
Therefore, $R (x, y, z) = (\frac{2 \times 4 + 1 \times 1}{2 + 1}, \frac{2 \times 3 + 1 \times 3}{2 + 1}, \frac{2 \times 1 + 1 \times 4}{2 + 1})$
$= (\frac{9}{3}, \frac{9}{3}, \frac{6}{3}) = (3, 3, 2)$

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Similar questions

Q. The ratio in which the plane

4 x + 5 y - 3 z = 8

divides the line joining the points

(- 2, 1, 5)

and

(3, 3, 2)

Q. Write the ratio in which the plane 4x + 5y − 3z = 8 divides the line segment joining the points (−2, 1, 5) and (3, 3, 2).

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.

Q. Find the coordinates of the point, which divides the line segment joining the points

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and

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Q. The xy-plane divides the line joining the points (−1, 3, 4) and (2, −5, 6)
(a) internally in the ratio 2 : 3
(b) externally in the ratio 2 : 3
(c) internally in the ratio 3 : 2
(d) externally in the ratio 3 : 2

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The point which divides the line joining the points (1,3,4) and (4,3,1) internally in the ratio 2:1, is

The correct option is E (3,3,2)Therefore, R(x,y,z)=(2×4+1×12+1,2×3+1×32+1,2×1+1×42+1)=(93,93,63)=(3,3,2)

The point which divides the line joining the points $(1, 3, 4)$ and $(4, 3, 1)$ internally in the ratio $2 : 1,$ is

The correct option is E $(3, 3, 2)$
Therefore, $R (x, y, z) = (\frac{2 \times 4 + 1 \times 1}{2 + 1}, \frac{2 \times 3 + 1 \times 3}{2 + 1}, \frac{2 \times 1 + 1 \times 4}{2 + 1})$
$= (\frac{9}{3}, \frac{9}{3}, \frac{6}{3}) = (3, 3, 2)$