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

Engineering

Mathematics

Equation of Straight Line in 3D

Section Formulae and Centres of a Triangle

theorem in space

Question

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)

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

(–3,3,2)

(3,3,2)

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