Question

Co-ordinate of a point equidistant from the points (0,0,0),

(a, 0, 0), (0, b, 0), (0, 0, c) is

• A. $\left( \frac{a}{4},\frac{b}{4},\frac{c}{4} \right)$
• B. $\left( \frac{a}{2},\frac{b}{4},\frac{c}{4} \right)$
• C. $\left( \frac{a}{2},\frac{b}{2},\frac{c}{2} \right)$
• D. (a, b, c)

Answer 1

Answer: (C)

$\left( \frac{a}{2},\frac{b}{2},\frac{c}{2} \right)$

Answer 2

The required point is the centre of the sphere through the given points.

Let the equation of sphere be

$x ^ { 2 } + y ^ { 2 } + 2 u x + 2 v y + 2 w z + d = 0$ .....(i)

Sphere (i) is passing through (0, 0, 0), (a, 0, 0), (0, b, 0) and (0, 0, c), $\therefore d = 0$

$a ^ { 2 } + 2 u a = 0 \Rightarrow u = - a / 2$

$b ^ { 2 } + 2 v b = 0 \Rightarrow v = - b / 2$

$c ^ { 2 } + 2 w c = 0 \Rightarrow w = - c / 2$

Therefore, centre of sphere is $( a / 2 , b / 2 , c / 2 )$, which is also the required point.