Yes. A vector is defined as having magnitude and direction (in reference to a fixed frame). Changing either of these properties redefines the vector.
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The magnitude of a vector is always treated as non negative and the minus sign indicates the reversal of that vector through an angle of 180 degree.
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If a linear transformation acts on a vector and the result is only a change in the vector's magnitude, not direction, that vector is called an eigenvector of that particular linear transformation, and the magnitude that the vector is changed by is called an eigenvalue of that eigenvector.Formulaically, this statement is expressed as Av=kv, where A is the linear transformation, vis the eigenvector, and k is the eigenvalue. Keep in mind that A is usually a matrix and k is a scalar multiple that must exist in the field of which is over the vector space in question.
Yes, a vector can be represented in terms of a unit vector which is in the same direction as the vector. it will be the unit vector in the direction of the vector times the magnitude of the vector.
Consider an equilateral triangle. If each vector started at the center of the triangle and went through a different vertex than the other two vectors then they would cancel. I believe in order for them to add to a null vector they must be co-planer.