Vectors A,B,C: Is Parallel Necessary?

Click For Summary
SUMMARY

The discussion clarifies that if two vectors A and B are perpendicular (A.B=0) and another vector A and C are also perpendicular (A.C=0), it does not necessitate that vectors B and C are parallel. This is illustrated using the Cartesian coordinate system where vectors along the X, Y, and Z axes demonstrate that perpendicularity does not imply parallelism. Specifically, in 2D, the relationship between vectors A, B, and C can exist without B being parallel to C.

PREREQUISITES
  • Understanding of vector mathematics, specifically dot products.
  • Familiarity with Cartesian coordinate systems.
  • Knowledge of geometric interpretations of vectors.
  • Basic concepts of linear independence and dependence.
NEXT STEPS
  • Study the properties of dot products in vector mathematics.
  • Explore the concept of linear independence in vector spaces.
  • Learn about vector projections and their geometric implications.
  • Investigate the implications of perpendicular vectors in higher dimensions.
USEFUL FOR

Students of mathematics, physics enthusiasts, and anyone studying linear algebra or vector calculus.

anigeo
Messages
83
Reaction score
0
say for example for 2 vectors A.B=0 and for another pair A.C=0.is it necessary that B is parallel to C.If yes how?
 
Physics news on Phys.org
As long as A and B are not zero, A.B=0 means A and B are perpendicular. A.C means A and C are perpendicular. That does not mean that B and C are parallel. Think of the three cartesian axes vectors X, Y, and Z: X.Y=0 and X.Z=0 but Y and Z are not parallel.
 
anigeo said:
say for example for 2 vectors A.B=0 and for another pair A.C=0.is it necessary that B is parallel to C.If yes how?

Only in 2D.
 

Similar threads

High School Confused about dot product multiplication
  • · Replies 33 ·
2
Replies
33
Views
5K
Undergrad Visualization of complex vectors and dot product
  • · Replies 14 ·
Replies
14
Views
4K
Undergrad Non orthogonal basis and the lines of its coordinate grid
  • · Replies 9 ·
Replies
9
Views
4K
Undergrad Is a 1x1 Matrix Considered a Scalar in Mathematics?
  • · Replies 12 ·
Replies
12
Views
4K
Undergrad Confused about dot product of a and b = |a||b| if theta = 0
  • · Replies 16 ·
Replies
16
Views
2K
MHB Find Dot Product Between Vector CD & Vector K
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Why is A.A = ||A||^2 in Vector Analysis?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Dot product, inner product, and projections
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad 2 interpretations of bra-ket expression: equal, & isomorphic, but...
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad The vector to which a dual vector corresponds
  • · Replies 13 ·
Replies
13
Views
4K