Question

The point equidistant from the points (a, 0, 0), (0, b, 0), (0, 0, c) and (0, 0, 0) is

• A. $(\frac{a}{3},\frac{b}{3},\frac{c}{3})$
• B. $(a,b,c)$
• C. $(\frac{a}{2},\frac{b}{2},\frac{c}{2})$
• D. $(\frac{a}{4},\frac{b}{4},\frac{c}{4})$

Answer 1

The correct option is C $(\frac{a}{2},\frac{b}{2},\frac{c}{2})$

Let point is $(\alpha ,\beta ,\gamma )$
$\therefore (\alpha -a{)}^2+{\beta }^2+{\gamma }^2={\alpha }^2+(\beta -b{)}^2+{\gamma }^2$
$={\alpha }^2+{\beta }^2+(\gamma -c{)}^2={\alpha }^2+{\beta }^2+{\gamma }^2$
We get, $\alpha =\frac{a}{2},\beta =\frac{b}{2}$and $\gamma =\frac{c}{2}$
$\therefore$ Required point is $(\frac{a}{2},\frac{b}{2},\frac{c}{2}).$