The triangle … in Example 7 has squared area …, from the…

These problems compute the areas of triangles.

The triangle $PQR$ in Example 7 has squared area $(\sqrt{3}/2{)}^2=(\frac{1}{2}{)}^2+(\frac{1}{2}{)}^2+(\frac{1}{2}{)}^2$, from the 3D version of Pythagoras in Remark 2. Find the area of $PQR$ when $P=(a,0,0)$, $Q=(0,b,0)$, and $R=(0,0,c)$. Check with $\frac{1}{2}|\mathbf{A}\times \mathbf{B}|$.

This exercise builds on another exercise in its source book, which isn't shown here.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §11.3 Cross Products and Determinants, #41