Let the position vectors of the points $$A,\,B,\,C$$   be $$\overrightarrow i + 2\overrightarrow j + 3\overrightarrow k ,\, - \overrightarrow i - \overrightarrow j + 8\overrightarrow k $$      and $$ - 4\overrightarrow i + 4\overrightarrow j + 6\overrightarrow k $$    respectively. Then the $$\Delta ABC$$   is :

Solution :
$$\eqalign{ & \overrightarrow {AB} = \overrightarrow {OB} - \overrightarrow {OA} \cr & = - \overrightarrow i - \overrightarrow j + 8\overrightarrow k - \left( {\overrightarrow i + 2\overrightarrow j + 3\overrightarrow k } \right) \cr & = - 2\overrightarrow i - 3\overrightarrow j + 5\overrightarrow k \cr} $$
Similarly, find $$\overrightarrow {BC} $$  and $$\overrightarrow {CA} .$$  Obtain $$\left| {\overrightarrow {AB} } \right| = \left| {\overrightarrow {BC} } \right| = \left| {\overrightarrow {CA} } \right|.$$