First slide

Introduction to 3-D Geometry

Question

The line segment joining the points $A (2, 3, 4)$ , $B (- 6, 5, - 4)$ intersect $x z -$ plane at

Very Easy

A

$(0, \frac{19}{5}, \frac{4}{5})$
B

$(0, 4, 5)$
C

$(- 4, 0, 16)$
D

$(14, 0, 16)$

Solution

The $x z -$ plane divides the line segment joining the points $A (x_{1}, y_{1}, z_{1})$ and $B (x_{2}, y_{2}, z_{2})$ in the ratio $- y_{1} : y_{2}$
The line segment joining the points $A (2, 3, 4)$ , $B (- 6, 5, - 4)$ intersect $x z -$ plane in the ratio $3 : 5$ externally
It implies that $P (\frac{- 18 - 10}{- 2}, \frac{15 - 15}{- 2}, \frac{- 12 - 20}{- 2}) = (14, 0, 16)$

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