Question

The plane $ax + by + cz = 1$meets the co-ordinate axes in A, B and C. The centroid of the triangle is

• A. $(3a,3b,3c)$
• B. $\left( \frac{a}{3},\frac{b}{3},\frac{c}{3} \right)$
• C. $\left( \frac{3}{a},\frac{3}{b},\frac{3}{c} \right)$
• D. $\left( \frac{1}{3a},\frac{1}{3b},\frac{1}{3c} \right)$

Answer 1

Answer: (D)

$\left( \frac{1}{3a},\frac{1}{3b},\frac{1}{3c} \right)$

Answer 2

Centroid is $\left( \frac { \frac { 1 } { a } + 0 + 0 } { 3 } , \frac { 0 + \frac { 1 } { b } + 0 } { 3 } , \frac { 0 + 0 + \frac { 1 } { c } } { 3 } \right)$ i.e.,$\left( \frac { 1 } { 3 a } , \frac { 1 } { 3 b } , \frac { 1 } { 3 c } \right)$.