The position vectors of two vertices and the centroid of a triangle are $$\overrightarrow i + \overrightarrow j ,\,2\overrightarrow i - \overrightarrow j + \overrightarrow k $$     and $$\overrightarrow k $$ respectively. The position vector of the third vertex of the triangle is :

Solution :
The positive vector of the centroid $$ = \frac{{\overrightarrow a + \overrightarrow b + \overrightarrow c }}{3},$$    where $$\overrightarrow a ,\,\overrightarrow b ,\,\overrightarrow c $$   are the position vectors of the vertices.
$$\therefore \,\overrightarrow k = \frac{{\overrightarrow i + \overrightarrow j + 2\overrightarrow i - \overrightarrow j + \overrightarrow k + \overrightarrow a }}{3}\,\,\,\,\,\therefore \overrightarrow a = - 3\overrightarrow i + 2\overrightarrow k $$