I assume you mean adding vectors?
Graphical: Draw them head-to-tail. Move the vectors around without rotating them.
Analytically: Separate the vectors into components. For example, in two dimensions, separate them into x and y components. Add the numbers for each dimension.
Coplanar :The vectors are in the same plane.Non coplanar :The vectors are not in the same plane.
Two-dimensional motion
when the vectors have the same direction
Coplanar vectors are vectors lying in the same plane.
Coplanar :The vectors are in the same plane.Non coplanar :The vectors are not in the same plane.
Coplanar :The vectors are in the same plane.Non coplanar :The vectors are not in the same plane.
Two vectors that lie along the same line-apex
No. For three vectors they must all lie in the same plane. Consider 2 vectors first. For them to resolve to zero, they must be in opposite direction and equal magnitude. So they will lie along the same line. For 3 vectors: take two of them. Any two vectors will lie in the same plane, and their resultant vector will also lie in that plane. Find the resultant of the first two vectors, and the third vector must be along the same line (equal magnitude, opposite direction), in order to result to zero. Since the third vector is along the same line as the resultant vector of the first two, then it must be in the same plane as the resultant of the first two. Therefore it lies in the same plane as the first two.
Two-dimensional motion
The orientation of the three vectors that sum to zero must be coplanar, contained in the same common plane, including being contained in a common line in a plane.
Coplanar :The vectors are in the same plane.Non coplanar :The vectors are not in the same plane.
Equal vectors are vectors having same direction of action or orientation as well as same magnitude. If two or more vectors have same magnitude but different direction then they cannot be called equal vectors. This shows that direction is important for equal vectors.
when the vectors have the same direction
when the vectors have the same direction
Coplanar vectors are vectors lying in the same plane.
Coplanar :The vectors are in the same plane.Non coplanar :The vectors are not in the same plane.
only if the vectors have the same direction