# vector projection

• Jan 15th 2008, 11:04 AM
viet
vector projection
[quote]Let T be the triangle with vertices at (4,10), (−8,8),(3,8). The area of T is = ? [quote]

i used the projection forumla and got the length of 1 side as: 4.2426 (not sure if that is right). should i do the same thing to find the other sides?
• Jan 15th 2008, 11:08 AM
topsquark
[QUOTE=viet;98972][quote]Let T be the triangle with vertices at (4,10), (−8,8),(3,8). The area of T is = ?
Quote:

i used the projection forumla and got the length of 1 side as: 4.2426 (not sure if that is right). should i do the same thing to find the other sides?
You can get the area of the triangle directly using Heron's formula.

-Dan
• Jan 15th 2008, 12:11 PM
Plato
It is really easy we recall a basic formula:
$\displaystyle A = \frac{1}{2}a \cdot b\sin \left( \phi \right) = \frac{1}{2}\left\| {a \times b} \right\|.$
That is one-half the dot product of the two vectors forming two sides of the triangle times the sine of the angle between. But sine is related to the cross product.