# scalar triple product

• Oct 2nd 2010, 11:30 PM
essence
scalar triple product

Hello everyone

could u plz help me to solve this question :

Use the scalar triple product to find the volume of the parallelopiped with vertices at
(−2,0,0),(2,0,0),(0,2,0),(4,2,0),(−1,1,4),(3,1,4), (1,3,4),(5,3,4) ?

thank u
• Oct 2nd 2010, 11:47 PM
earboth
Quote:

Originally Posted by essence

Hello everyone

could u plz help me to solve this question :

Use the scalar triple product to find the volume of the parallelopiped with vertices at
(−2,0,0),(2,0,0),(0,2,0),(4,2,0),(−1,1,4),(3,1,4), (1,3,4),(5,3,4) ?

thank u

1. Draw a rough sketch of the parallelepiped.

2. Choose one vertex (for instance (2, 0, 0)) and calculate the vectors representing the edges of the parallelepiped starting from (2, 0, 0).

3. Use the formula

$\displaystyle V=\vec a \cdot (\vec b \times \vec c)$

to calculate the volume of this solid.
• Oct 3rd 2010, 12:05 AM
essence
thanks a lot honey

do u mean i have to choose 3 vectors a , b and c then apply in V??

for example: a=(2, 0,0) , b=(0, 2 ,0) c=(5,3,4) like that or not?

could u plz give example? I'm really very stack

thank u
• Oct 3rd 2010, 03:20 AM
HallsofIvy
No, those are points not vectors. Use the vectors from (2, 0, 0) to three "adjacent" points. ("Adjacent" meaning there is an edge of the parallelpiped between the point and (2, 0,0).)
• Oct 3rd 2010, 05:18 AM
essence
ok it's clear now thanks a lot honey