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Question

(B) The formula for the coordinates of a point dividing the line segment joining $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ in the ratio $m:n$ externally

Vedclass · Accepted Answer

$(1, 10, 1)$

Vedclass · Answer

(B) The formula for the coordinates of a point dividing the line segment joining $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ in the ratio $m:n$ externally is given by: $\left(\frac{mx_2 - nx_1}{m - n}, \frac{my_2 - ny_1}{m - n}, \frac{mz_2 - nz_1}{m - n}\right)$ Given points are $(2, 3, 4)$ and $(3, -4, 7)$ with ratio $m:n = 2:4$. Substituting the values: $x = \frac{2(3) - 4(2)}{2 - 4} = \frac{6 - 8}{-2} = \frac{-2}{-2} = 1$ $y = \frac{2(-4) - 4(3)}{2 - 4} = \frac{-8 - 12}{-2} = \frac{-20}{-2} = 10$ $z = \frac{2(7) - 4(4)}{2 - 4} = \frac{14 - 16}{-2} = \frac{-2}{-2} = 1$ Thus,the coordinates are $(1, 10, 1)$.

The coordinates of the point which divides the line joining the points $(2, 3, 4)$ and $(3, -4, 7)$ in the ratio $2:4$ externally are:

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