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In math and physics, displacement and velocity are examples of vectors. The definition of a vector is that it is quantity that has both direction and magnitude. A vector is represented by an arrow that shows the direction of the quantity and a length which is the magnitude.
In geometry a vector is used to make the equations easier to understand and to figure out. Velocity and force are examples of vectors. For a vector to be coplanar there must be two or more and they must be linearly dependent. Coplanar vectors have proportional components and their rank is 2.
No, the sum of two vectors cannot be equal to either of the vectors individually. In vector addition, the resultant vector is determined by the magnitude and direction of the individual vectors. The sum of two vectors represents the combination of their effects, resulting in a new vector with different properties than the original vectors.
The zero vector is not perpendicular to all vectors, but it is orthogonal to all vectors.
A unit vector is a vector whose magnitude is one. Vectors can have magnitudes that are bigger or smaller than one so they would not be unit vectors.