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.
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Non-proportional vectors are vectors that do not have a constant scalar multiple relationship between them. In other words, they do not lie on the same line or in the same direction. Non-proportional vectors are linearly independent and have different magnitudes and directions.
To add vectors on the same line, simply add their components together. If you have two vectors represented as (a1, a2) and (b1, b2), their sum would be (a1 + b1, a2 + b2). This is known as the component method of vector addition.
The term for vectors pointing in different directions is called linearly independent vectors. These vectors do not lie on the same line or plane, and they provide unique information to describe a space.
Two vectors which do not lie along the same line represent motion in two different directions. This indicates that an object is moving simultaneously in more than one direction.
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Coplanar vectors lie within the same plane, meaning they can be represented by arrows with their tails at the same point. Collinear vectors, on the other hand, lie along the same line, meaning they have the same or opposite directions. In essence, coplanar vectors can be parallel or intersecting within the same plane, while collinear vectors are always parallel or antiparallel along the same line.
Non-proportional vectors are vectors that do not have a constant scalar multiple relationship between them. In other words, they do not lie on the same line or in the same direction. Non-proportional vectors are linearly independent and have different magnitudes and directions.
To add vectors on the same line, simply add their components together. If you have two vectors represented as (a1, a2) and (b1, b2), their sum would be (a1 + b1, a2 + b2). This is known as the component method of vector addition.
The term for vectors pointing in different directions is called linearly independent vectors. These vectors do not lie on the same line or plane, and they provide unique information to describe a space.
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 vectors which do not lie along the same line represent motion in two different directions. This indicates that an object is moving simultaneously in more than one direction.
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