question_answer

Let a, b, c be the position vectors of the vertices of a triangle ABC. The vector area of triangle ABC is   [MP PET 1990; EAMCET 2003]

A)                 \[\mathbf{a}\times \mathbf{b}+\mathbf{b}\times \mathbf{c}+\mathbf{c}\times \mathbf{a}\]

B)                 \[\frac{1}{4}(\mathbf{a}\times \mathbf{b}+\mathbf{b}\times \mathbf{c}+\mathbf{c}\times \mathbf{a})\]

C)                 \[\frac{1}{2}(\mathbf{a}\times \mathbf{b}+\mathbf{b}\times \mathbf{c}+\mathbf{c}\times \mathbf{a})\]

D)                 \[\mathbf{b}\times \mathbf{a}+\mathbf{c}\times \mathbf{b}+\mathbf{a}\times \mathbf{c}\]