Help with vectors

Question

Determine the area of the triangle formed by the points A (-1, 2, 1), B (-1, 0, 0) and C (3, -1, 4)

Answer 1

The easiest way I know to find this area is the determinant

(1/2) |x₁ y₁ 1|

|x₂ y₂ 1|

|x₃ y₃ 1|

This formula comes about by breaking the area into 3 separate triangles and calculating those areas.

As a last resort you can use the distance formula to calculate the lengths of the 3 sides and use Heron's formula.