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(B) Let the points be $A(2, 4, 5)$ and $B(3, 5, -4)$. The ratio is $m : n = -2 : 3$. Using the section formula,the coordinates of the point $P(x, y, z

Vedclass · Accepted Answer

$YOZ$ plane

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(B) Let the points be $A(2, 4, 5)$ and $B(3, 5, -4)$. The ratio is $m : n = -2 : 3$. Using the section formula,the coordinates of the point $P(x, y, z)$ are given by: $x = \frac{mx_2 + nx_1}{m + n} = \frac{(-2)(3) + (3)(2)}{-2 + 3} = \frac{-6 + 6}{1} = 0$ $y = \frac{my_2 + ny_1}{m + n} = \frac{(-2)(5) + (3)(4)}{-2 + 3} = \frac{-10 + 12}{1} = 2$ $z = \frac{mz_2 + nz_1}{m + n} = \frac{(-2)(-4) + (3)(5)}{-2 + 3} = \frac{8 + 15}{1} = 23$ The coordinates of the point are $(0, 2, 23)$. Since the $x$-coordinate is $0$,the point lies on the $YOZ$ plane.

The point which divides the line segment joining the points $(2, 4, 5)$ and $(3, 5, -4)$ in the ratio $-2 : 3$ lies on which of the following?

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