If a plane meets the coordinate axes at A, B and C, in such a way that the centroid of ΔABC is at the point (1, 2,3), the equation of the plane is
Answer & explanation
Correct answer: option 2
Let the equation of the required plane be $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}= 1.$ This meets the coordinate axes at A(a, 0, 0) B(0, b, 0) and C(0, 0, c) the coordinates of the centroid of ΔABC are $(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}).$
$∴ \frac{a}{3}=1, \frac{b}{3}=2$ and $\frac{c}{3}= 3⇒ a = 3, b = 6$ and $c = 9$
Hence, the equation of the plane is $\frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1.$