Question

Using vectors, find the area of ΔABC whose vertices are A(3, −1, 2), B(1, −1, −3) and C(4, −3, 1)

Answer 1

Through the vertices we get the adjacent vectors as,

vector AB = -2i+0j - 5k and vector AC = i - 2j - k

The area of the triangle = vector |a x b|/2, where a and b are it’s adjacent sides vectors.

Thus, substituting the values of a₁, a₂, a₃ and b₁, b₂ and b₃, in equation (i) we get