Find the coordinates of the point which divid | vedclass

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(A) Let the points be $A(1, -2, 3)$ and $B(3, 4, -5)$. The point $P(x, y, z)$ divides the line segment $AB$ externally in the ratio $m:n = 2:3$.The se

Vedclass · Accepted Answer

$(-3, -14, 19)$

Vedclass · Answer

(A) Let the points be $A(1, -2, 3)$ and $B(3, 4, -5)$. The point $P(x, y, z)$ divides the line segment $AB$ externally in the ratio $m:n = 2:3$.The section formula for external division is given by:$x = \frac{mx_2 - nx_1}{m - n}, y = \frac{my_2 - ny_1}{m - n}, z = \frac{mz_2 - nz_1}{m - n}$Substituting the values $m=2, n=3, x_1=1, y_1=-2, z_1=3, x_2=3, y_2=4, z_2=-5$:$x = \frac{2(3) - 3(1)}{2 - 3} = \frac{6 - 3}{-1} = -3$$y = \frac{2(4) - 3(-2)}{2 - 3} = \frac{8 + 6}{-1} = -14$$z = \frac{2(-5) - 3(3)}{2 - 3} = \frac{-10 - 9}{-1} = 19$Thus,the coordinates of the point are $(-3, -14, 19)$.

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

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