# Area of triangle formed by 2 vectors

1. Apr 24, 2010

### heidihiiiiiii

1. The problem statement, all variables and given/known data
I have a triangle ABC formed by vectors a = ( 2, 10, 25 ) and b = ( 5, 4, -2 ) attached at a point P.
And I have to calculate the area of the triangle ABC.

2. Relevant equations
I'm pretty certain that I need to find the area of the parellogram and then half it.
So I need to find the cross product, by calculating the determinant.

3. The attempt at a solution
Calculating the determinant I got
-120 i + 129 j - 42 k
so does this mean i square those and take the square root of them to find the area of the parellogram and then half it...
= 181.121
=> area of triangle = 90.56

2. Apr 24, 2010

### Dick

Sure, you're doing it right.

3. Apr 24, 2010

### heidihiiiiiii

Thanks..I thought I was on the right lines, just needed reassuring :)

I got the area of the traingle to be 81root5 / 2

But now I need to calculate the length of the height PM (where PM perpendicular to BC and the point M belongs to the line BC)

I'm guessing as I know the area and 2 vectors I can take it from there...but I really have no idea....

4. Apr 24, 2010

### Dick

Use |axb|=|a|*|b|*sin(t), where t is the smaller angle between the vectors a and b. Find t and use trig.