Vectors A,B,C: Is Parallel Necessary?

In summary, if two vectors A and B have a dot product of 0, it means they are perpendicular. However, this does not necessarily mean that B is parallel to C, even if A and C also have a dot product of 0. This concept only applies in 2D, as in 3D there can be cases where three vectors with perpendicular dot products are not parallel.
  • #1
anigeo
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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?
 
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  • #2
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.
 
  • #3
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.
 

1. What is the difference between parallel and non-parallel vectors?

Parallel vectors are two or more vectors that have the same direction and are either the same length or are scalar multiples of each other. Non-parallel vectors do not have the same direction and cannot be expressed as scalar multiples of each other.

2. Is it possible for three vectors to be parallel but not coplanar?

No, if three vectors are parallel, it means they lie on the same plane. Therefore, they must be coplanar.

3. How do you determine if two vectors are parallel?

If two vectors are parallel, their direction vectors must be proportional. This means that if you express both vectors in terms of unit vectors, the coefficients of the unit vectors must be equal.

4. Can non-parallel vectors be considered as parallel in certain cases?

No, non-parallel vectors can never be considered as parallel. Parallel vectors must have the same direction and be either the same length or scalar multiples of each other.

5. Is it necessary for vectors to be parallel in order to be added or subtracted?

No, vectors do not have to be parallel in order to be added or subtracted. The result of adding or subtracting non-parallel vectors will be a new vector with a different direction and magnitude.

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