Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §11.3 Cross Products and Determinants, #42 · Multivariable Calculus · Vectors & geometry

A triangle in the … plane has corners at … and

These problems compute the areas of triangles.

A triangle in the $x y$ plane has corners at $(a_{1}, b_{1}), (a_{2}, b_{2})$ and $(a_{3}, b_{3})$ . Its area $A$ is half the area of a parallelogram. Find two sides of the parallelogram and explain why
$A = \frac{1}{2} ∣ (a_{2} - a_{1}) (b_{3} - b_{1}) - (a_{3} - a_{1}) (b_{2} - b_{1}) ∣.$

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §11.3 Cross Products and Determinants, #42

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