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

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

KEAMKEAM 2012Introduction to Three Dimensional Geometry

Solution:

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