Question

If $A(1,2,3),B(2,3,1),C(3,1,2)$ then the length of the altitude through $C$ is

• A. $3$
• B. $3\sqrt{3}$
• C. $3\sqrt{2}$
• D. $\frac{3}{\sqrt{2}}$

Answer 1

The correct option is D $\frac{3}{\sqrt{2}}$

So $△ABC$ is equilateral
So length of median $=$ length of attitude
$D$ is mid point of $AB$
P.V of $D=(\frac{3}{2},\frac{5}{2},2)$
$CD=\sqrt{\frac{9}{4}+\frac{9}{4}}$
$=\frac{3}{\sqrt{2}}$