Identifying Collinear, Parallel & Coplanar Vectors

[dcl]

Heyas.

I'm need help knowing what is meant by the term Collinear, parrallel and coplanar vectors...

How do I identify collinear, parallel or coplanar vectors?

If 2 vectors are parallel, say 'a' and 'b' then if a = k*b they are parallel?

I really need some help understanding these terms and definitions.

Thanks :D

 

[sridhar_n]

Vectors...

Hi,

Before answering ur qn, let me just tell u these...

2 points are said to be colinear if they lie on the same line.
---A---->----B---> Here in this diagram, points A and B lie on the same line and hence are colinear. Thus when 2 vectors act along the same line, then they are said to be colinear.

When 2 vectors act along the same line but have a separation between them, they are said to be Parallel. i.e Parallel vectors have the same phase, but different magnitudes. That is why when 2 vectors A and B are parallel, then, A=kB, where, K is a constant.

--------A---------> Here A and B are parallel.
----------B--------->

Note: Colinear Vectors are also Parallel vectors except that they lie on the same line.

Mathematically speaking, when 2 vectors are parallel, the dot product of the vectors are 1 and their cross product is zero.(As angle between them is zero)

2 vectors are said to be Co planar if they act in the same plane but they have diferent/same magnitudes and phases.

Hope u Understood.

Sridhar

 

[dcl]

Thanks for that :)
knowing that the dot product of parallel vectors is 1 should help me out heaps. That isn't mentioned in my textbook anywhere.

That should have cleared that up for me. :)

 

[HallsofIvy]

Mathematically speaking, when 2 vectors are parallel, the dot product of the vectors are 1 and their cross product is zero.(As angle between them is zero)

When two vectors are parallel, their cross product is zero (although that would be the hard way to determine parallelism) but their dot product is NOT necessarily 1. The dot product of two parallel vectors is the product of their lengths.

If 2 vectors are parallel, say 'a' and 'b' then if a = k*b they are parallel?

I think what you mean to say here is that "two vectors are parallel if and only if one is a multiple of the other". That is true and is the easiest way to determine whether two vectors are parallel.

 

[ankitv]

vectors

How to differentiate between parallel vectors & collinear vectors?