Question

If from a point $P(a,b,c)$ perpendicular $PA$ and $PB$ are drawn to $yz$ and $zx$ planes, find the equation of the plane $OAB$:

• A. $\frac{x}{a}+\frac{y}{b}-\frac{z}{c}=0$
• B. $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=0$
• C. xa−yb−z
• D. None of these

Answer 1

The correct option is A $\frac{x}{a}+\frac{y}{b}-\frac{z}{c}=0$

The coordinates of $A$ and $B$ are $(0,b,c)$ and $(a,0,c)$ respectively.

The equation of the plane passing through $O(0,0,0),A(0,b,0)$ and $B(a,0,c)$ is given by

$\left|\begin{array}{ccc}x-0& y-0& z-0\\ 0-0& b-0& c-0\\ a-0& 0-0& c-0\end{array}\right|=0\Rightarrow bcx+acy-abz=0$

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