The co-ordinates of the point where the line through the points A(3,4,1) and B(5,1,6) crosses the xy-plane

A
$(\frac{13}{5}, 0, \frac{23}{5})$
B
$(\frac{13}{5}, \frac{23}{5}, \frac{6}{5})$
C
$(\frac{13}{5}, \frac{23}{5}, 0)$
D
$(\frac{13}{3}, \frac{23}{3}, 0)$

Solution:

The xy - plane cuts the line segment joining the points $A (x_{1}, y_{1}, z_{1}), B (x_{2}, y_{2}, z_{2})$ in the ratio $- z_{1} : z_{2}$

Hence, the xy- plane divides the line segment joining the points $A (3, 4, 1)$ and $B (5, 1, 6)$ in the ratio $- 1 : 6$

The coordinates of the point which divides the line segment $A B$ in the ratio $1 : 6$ externally is $(\frac{5 - 18}{- 5}, \frac{1 - 24}{- 5}, 0) = (\frac{13}{5}, \frac{23}{5}, 0)$

The co-ordinates of the point where the line through the points $A (3, 4, 1)$ and $B (5, 1, 6)$ crosses the xy-plane

Solution:

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