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(B) The section formula for a point dividing the line segment joining $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ in the ratio $m:n$ is given by $\left( \

Vedclass · Accepted Answer

$\left( -2, \frac{25}{2}, \frac{-3}{2} \right)$

Vedclass · Answer

(B) The section formula for a point dividing the line segment joining $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ in the ratio $m:n$ is given by $\left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}, \frac{mz_2 + nz_1}{m+n} \right)$.Here,$(x_1, y_1, z_1) = (1, 2, 3)$,$(x_2, y_2, z_2) = (3, -5, 6)$,$m = 3$,and $n = -5$.The sum of the ratio is $m + n = 3 - 5 = -2$.Calculating the $x$-coordinate: $x = \frac{3(3) + (-5)(1)}{-2} = \frac{9 - 5}{-2} = \frac{4}{-2} = -2$.Calculating the $y$-coordinate: $y = \frac{3(-5) + (-5)(2)}{-2} = \frac{-15 - 10}{-2} = \frac{-25}{-2} = \frac{25}{2}$.Calculating the $z$-coordinate: $z = \frac{3(6) + (-5)(3)}{-2} = \frac{18 - 15}{-2} = \frac{3}{-2} = -\frac{3}{2}$.Thus,the point is $\left( -2, \frac{25}{2}, -\frac{3}{2} \right)$,which matches option $B$.

The point dividing the line segment joining the points $(1, 2, 3)$ and $(3, -5, 6)$ in the ratio $3: -5$ is

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