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

Given,

A triangle with vertices A (1, 1, 2), B (2, 3, 5) and C (1, 5, 5)

Key Point: Area of a triangle (ΔABC) is given by – Area =

We are given with the coordinates, or we can say the P.V of points A, B and C.

∴ We can say that –

∴ )î

⇒

Similarly,

∴ Area of required triangle =

So, first, we find the magnitude of cross product and then we will apply the formula-

∴ =

Expanding about 1^st row –

⇒

∴ || =

∴ Area of required triangle =