Area of triangle formed by 2 vectors

[heidihiiiiiii]

Homework Statement

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.

Homework 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.

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

 

[Dick]

Sure, you're doing it right.

 

[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...

 

[Dick]

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