# [SOLVED] Find volume of a parallelepiped with 3 sides

• Mar 4th 2010, 12:48 PM
thekrown
[SOLVED] Find volume of a parallelepiped with 3 sides
We have sides u, v, w and I must find the volume of the parallelepiped.

u = (3,1,2)
v = (4,5,1)
w = (1,2,4)

The V = | u . (v x w) |

In plain English I think this means I must find the absolute value of the dot product of u and (vxw). (v x w) is a cross product.

So I calculated the cross product of v and w and it gave me

|square root 18^2 + 15^2 + 3^2|.

I really don't know what to do at this point, any help?
• Mar 4th 2010, 01:09 PM
tonio
Quote:

Originally Posted by thekrown
We have sides u, v, w and I must find the volume of the parallelepiped.

u = (3,1,2)
v = (4,5,1)
w = (1,2,4)

The V = | u . (v x w) |

In plain English I think this means I must find the absolute value of the dot product of u and (vxw). (v x w) is a cross product.

So I calculated the cross product of v and w and it gave me

|square root 18^2 + 15^2 + 3^2|.

I really don't know what to do at this point, any help?

The cross product is (18,-15,3) , and this inner multiplied by u gives 45...

Tonio