# Math Help - scalar triple product

1. ## 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

2. 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

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

to calculate the volume of this solid.

3. 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

4. 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).)

5. ok it's clear now thanks a lot honey