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Question

(A) Let $P(x, y, z)$ be the point which divides the line segment joining $A(1, -2, 3)$ and $B(3, 4, -5)$ internally in the ratio $m:n = 2:3$. Using th

Vedclass · Accepted Answer

$\left(\frac{9}{5}, \frac{2}{5}, -\frac{1}{5}\right)$

Vedclass · Answer

(A) Let $P(x, y, z)$ be the point which divides the line segment joining $A(1, -2, 3)$ and $B(3, 4, -5)$ internally in the ratio $m:n = 2:3$. Using the section formula: $x = \frac{mx_2 + nx_1}{m+n} = \frac{2(3) + 3(1)}{2+3} = \frac{6+3}{5} = \frac{9}{5}$ $y = \frac{my_2 + ny_1}{m+n} = \frac{2(4) + 3(-2)}{2+3} = \frac{8-6}{5} = \frac{2}{5}$ $z = \frac{mz_2 + nz_1}{m+n} = \frac{2(-5) + 3(3)}{2+3} = \frac{-10+9}{5} = -\frac{1}{5}$ Thus,the required point is $\left(\frac{9}{5}, \frac{2}{5}, -\frac{1}{5}\right)$.

Find the coordinates of the point which divides the line segment joining the points $(1, -2, 3)$ and $(3, 4, -5)$ in the ratio $2:3$ internally.

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