Practicing Success
If from a point (a, b, c) perpendicular PA, PB are drawn to YZ and ZX planes, then the equation of the plane OAB is |
$bcx + cay + abz = 0$ $bcx + cay + abz = 0$ $bcx - cay + abz = 0$ $-bcx + cay + abz = 0$ |
$bcx + cay + abz = 0$ |
The coordinates of A and B are (0, b, c) and (a, 0, c) respectively. The equation of a plane passing through O(0, 0, 0) is $Px + Qy + Rz = 0 $ ..........(i) It passes through A and B $∴ P × 0 + Q × b + R × c = 0 $ and, $ P × a + Q × 0 + R × c = 0 $ $⇒ \frac{P}{bc}=\frac{Q}{ac}=\frac{R}{-ab}$ Substituting the values of P, Q and R in (i), we get $bcx + cay + abz = 0$ |