Find the area of the triangle with vector?

Question

Find the given points A, B, and C find the area of the triangle with vertices A, B, and C.

A(2, 8, 3), B(9, 16, 4), C(4, 9, 4).

The area is ____.

Answer 1

WE create vectors: AB = <7, 8, 1> and AC = <2, 1, 1>.

Now area S = 1/2IABxACI;

Ii j kI

ABxAC = I7 8 1I = 7i - 5j - 9k

I2 1 1I

Then area of triangle S = 1/2(7² +(-5)² + (-9)²)^1/2 = 6.22495