Find the coordinate of point where the line through $(3, 4, 1)$ & $(5, 1, 6)$ crosses XY-plane.The plane divides line in ratio 1:-6

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Solution

Given,
$\begin{matrix} x, y p l a n e d i v i d s ¯ ¯¯¯¯¯¯ ¯ A B i n t h e r a t i o, z_{1} : z_{2} 1 : - 6 n - 1 : 6 T h e l i n e t h r o u g h : A (3, 4, 1) B (5, 1, 6) c r o s s e s X Y p l a n e, \frac{(- 1) (5) + (6) (3)}{- 1 + 6}, \frac{(- 1) (1) + (6) (4)}{- 1 + 6}, \frac{(- 1) (6) + (6) (1)}{- 1 + 6} \frac{- 5 + 18}{5}, \frac{- 1 + 24}{5}, \frac{- 6 + 6}{5} \frac{13}{5}, \frac{23}{5}, 0 \end{matrix}$

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A = (3, 4, 1)

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Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the ZX-plane.

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