Using vectors, find the area of the triangle ABC with vertices A(1, 2, 3), B(2, – 1, 4) and C(4, 5, – 1).

We have,

The coordinates of points A, B and C are (1, 2, 3), (2, -1, 4) and (4, 5, -1) respectively.

We need to find the area of this triangle ABC.

We have the formula given as,

…(i)

Let us find out and first.

We can say,

Position vector of A

Position vector of B

Position vector of C

For :

Position vector of B-Position vector of A

For :

Position vector of C-Position vector of A

Now, substitute values of and in . We can find out as,

And,

From equation (i), we get

Thus, area of ∆ABC is .