The point dividing the join of (3, -2, 1) and | vedclass

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(B) Let the required point be $P$. By the section formula,the coordinates of point $P$ dividing the line segment joining $(x_1, y_1, z_1)$ and $(x_2,

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$(1, 0, 5)$

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(B) Let the required point be $P$. By the section formula,the coordinates of point $P$ dividing the line segment joining $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ in the ratio $m:n$ are given by:$P = \left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}, \frac{mz_2 + nz_1}{m+n}\right)$Here,$(x_1, y_1, z_1) = (3, -2, 1)$,$(x_2, y_2, z_2) = (-2, 3, 11)$,$m = 2$,and $n = 3$.Substituting these values into the formula:$P = \left(\frac{2(-2) + 3(3)}{2+3}, \frac{2(3) + 3(-2)}{2+3}, \frac{2(11) + 3(1)}{2+3}\right)$$P = \left(\frac{-4 + 9}{5}, \frac{6 - 6}{5}, \frac{22 + 3}{5}\right)$$P = \left(\frac{5}{5}, \frac{0}{5}, \frac{25}{5}\right)$$P = (1, 0, 5)$

The point dividing the join of $(3, -2, 1)$ and $(-2, 3, 11)$ in the ratio $2:3$ is

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