First slide

Straight lines in 3D

Question

From the point P(a, b, c),let perpendiculars PL and PM be drawn to YOZ and ZOX planes, respectively. Then the
equation of the plane OLM is

Moderate

A

$\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 0$
B

$\frac{x}{a} + \frac{y}{b} - \frac{z}{c} = 0$
C

$\frac{x}{a} - \frac{y}{b} - \frac{z}{c} = 0$
D

$\frac{x}{a} - \frac{y}{b} + \frac{z}{c} = 0$

Solution

Coordinates of L and M are (0, b, c) and (a,0, c), respectively.
Therefore, the equation of the plane passing through (0, 0, 0), (0, b, c) and (a, 0, c) is
$|\begin{array}{ccc} x - 0 & y - 0 & z - 0 \\ 0 & b & c \\ a & 0 & c \end{array}| = 0 or \frac{x}{a} + \frac{y}{b} - \frac{z}{c} = 0$

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