Find the coordinates of the point which divid | vedclass

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Question

(A) The coordinates of a point $R$ that divides the line segment joining points $P(x_1, y_1, z_1)$ and $Q(x_2, y_2, z_2)$ internally in the ratio $m:n

Vedclass · Accepted Answer

$\left(-\frac{4}{5}, \frac{1}{5}, \frac{27}{5}\right)$

Vedclass · Answer

(A) The coordinates of a point $R$ that divides the line segment joining points $P(x_1, y_1, z_1)$ and $Q(x_2, y_2, z_2)$ internally in the ratio $m:n$ are given by the section formula:$\left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}, \frac{mz_2 + nz_1}{m+n}\right)$Given points are $P(-2, 3, 5)$ and $Q(1, -4, 6)$ with ratio $m:n = 2:3$.Substituting the values:$x = \frac{2(1) + 3(-2)}{2+3} = \frac{2 - 6}{5} = -\frac{4}{5}$$y = \frac{2(-4) + 3(3)}{2+3} = \frac{-8 + 9}{5} = \frac{1}{5}$$z = \frac{2(6) + 3(5)}{2+3} = \frac{12 + 15}{5} = \frac{27}{5}$Thus,the coordinates of the required point are $\left(-\frac{4}{5}, \frac{1}{5}, \frac{27}{5}\right)$.

Find the coordinates of the point which divides the line segment joining the points $(-2, 3, 5)$ and $(1, -4, 6)$ in the ratio $2:3$ internally.

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