Find the coordinates of the point which divid | vedclass

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Question

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

Vedclass · Accepted Answer

$(-8, 17, 3)$

Vedclass · Answer

(A) The coordinates of point $R$ that divides the line segment joining points $P(x_1, y_1, z_1)$ and $Q(x_2, y_2, z_2)$ externally in the ratio $m:n$ are given by the 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: $x = \frac{2(1) - 3(-2)}{2-3} = \frac{2 + 6}{-1} = -8$ $y = \frac{2(-4) - 3(3)}{2-3} = \frac{-8 - 9}{-1} = \frac{-17}{-1} = 17$ $z = \frac{2(6) - 3(5)}{2-3} = \frac{12 - 15}{-1} = \frac{-3}{-1} = 3$ Thus,the coordinates of the required point are $(-8, 17, 3)$.

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

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