How to write an equation for plane, which includes dots with radius-vectors $\mathbf r_{1}, \mathbf r_{2}, \mathbf r_{3}$ that do not lie on a straight line? The answer is
$ (\mathbf r, ([\mathbf r_{3} , \mathbf r_{1}] + [\mathbf r_{2} , \mathbf r_{3}] + [\mathbf r_{1} , \mathbf r_{2}]) ) = (\mathbf r_{1}, [\mathbf r_{2}, \mathbf r_{3}]). $
How to explain it?