Question

Find a unit vector perpendicular to the plane containing the point (a, 0, 0), (0, b, 0), and (0, 0, c). What is the area of the triangle with these vertices?

Answer 1

The position vectors \(\overline{p},\) \(\overline{q},\) \(\overline{r}\) of the points A(a, 0, 0), B(0, b, 0), C(0, 0, c) are

\(\overline{AB} \times \overline{BC}\) is perpendicular to the plane containing A, B, C.

\(\therefore\) the required unit vector