Find the area of the triangle with the given vertices. use the fact that the area of the triangle having u and v as adjacent sides is given by a = 1 2 u × v . (3, 5, 9), (5, 5, 0), (−4, 0, 2)

The area of the triangle is

Step-by-step explanation:

Using the fact that the area of the triangle having u and v as adjacent sides is given by

We know that we want to take a cross product to compute the area of the triangle, but we need to be careful because it doesn't make sense if we take the cross product of points.

The first step is to build some vectors that describe this triangle.

According with the graph we can build the vectors:

and

The vector is the difference of point B minus point A

and the vector is the difference of point C minus point A

Next we need to find the cross product of this vectors.

This is the definition of cross product of two vectors in space:

Let and be vectors in space. The cross product of and is the vector

Applying this definition we get

The area of the triangle is

4 + 5 7/9= 9 7/9

step-by-step explanation:

the discriminant is 64 + 4*1*12 = 112

this is prime.

step-by-step explanation: