The Scalar Triple Product

  • Thread starter PFuser1232
  • Start date
  • #1
479
20

Main Question or Discussion Point

The volume of a triangular prism is given by:

v = ½ |ab x c|

Where b and c are two of the sides of the triangular face of the prism, and a is the length of the prism.

The volume of a rectangular/parallelogram-based pyramid is given by:

V = ⅓ |a • b x c|

My question is, what are a, b, and c?
Is it necessary, in general, that b and c be the lengths of two of the sides of the base?
 

Answers and Replies

  • #2
11,499
5,041
they are vectors that are the edges of a parallelogram when placed with tails coming from the same vertex.

tripprod0x_thumb.png
 
  • #3
1,007
76
Well this topic regenerated the doubt that was in my mind some time ago.
Volume of parallelopiped is
[a b c]
Then how Volume of tetrahedron is
1/6 [a b c]
 
  • #5
479
20
So the permutations of vectors in the triple product doesn't really matter, provided the absolute value is taken.
What matters is that they should be three vectors meeting at any vertex. Correct?
 
  • #6
11,499
5,041
Yes and that defines the parallel piped too.
 

Related Threads on The Scalar Triple Product

  • Last Post
Replies
2
Views
2K
Replies
4
Views
1K
Replies
4
Views
865
Replies
3
Views
2K
  • Last Post
Replies
9
Views
987
  • Last Post
Replies
13
Views
841
  • Last Post
Replies
9
Views
719
Replies
5
Views
733
Replies
10
Views
1K
Replies
6
Views
600
Top