Question

If the distance of a point $(a,a,a)$ from the origin is $\sqrt{108}$, then the value of $a$ is

• A. $9$
• B. $6$
• C. $-9$
• D. $-6$

Answer 1

Answer: (B), (D)

$6$
$-6$

Distance between $(x_1,y_1)$ and $(x_2,y_2)$ is $\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}$

Distance between $(0,0,0)$ and $(a,a,a)$ is $\sqrt{{(a-0)}^2+{(a-0)}^2+{(a-0)}^2}$

$\sqrt{3\times {\left(a\right)}^2}=\sqrt{108}=6\sqrt{3}\Rightarrow a=\pm 6$