XOZ-plane divides the line segment joining th | vedclass

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(C) Let the $XOZ$-plane divide the line segment joining the points $A(2, 3, 1)$ and $B(6, 7, 1)$ in the ratio $m: n$. Using the section formula, the c

Vedclass · Accepted Answer

$-3$

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(C) Let the $XOZ$-plane divide the line segment joining the points $A(2, 3, 1)$ and $B(6, 7, 1)$ in the ratio $m: n$. Using the section formula, the coordinates of the point of division are given by: $\left(\frac{m(6)+n(2)}{m+n}, \frac{m(7)+n(3)}{m+n}, \frac{m(1)+n(1)}{m+n}\right)$ Since the point lies on the $XOZ$-plane, its $y$-coordinate must be zero. Therefore, $\frac{7m + 3n}{m+n} = 0$. $7m + 3n = 0$ $7m = -3n$ $\frac{m}{n} = -\frac{3}{7}$ Thus, the ratio is $-3: 7$.

$XOZ$-plane divides the line segment joining the points $(2, 3, 1)$ and $(6, 7, 1)$ in the ratio: (in $: 7$)

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