Area of triangle formed by 2 vectors

  • #1

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
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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Sure, you're doing it right.
 
  • #3
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
Dick
Science Advisor
Homework Helper
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Use |axb|=|a|*|b|*sin(t), where t is the smaller angle between the vectors a and b. Find t and use trig.
 

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