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Any vector can be fully represented by providing its magnitude and a unit vector along its direction.






Addition of two vectors is accomplished by laying the vectors head to tail in sequence to create a triangle such as is shown in the figure.

The following rules apply in vector algebra.

where P and Q are vectors and a is a scalar.

Unit vectors:

A unit vector is a vector of unit length. A unit vector is sometimes denoted by replacing the arrow on a vector with a " ^" (i.e., ). Therefore,

Any vector can be made into a unit vector by dividing it by its length.

Any vector can be fully represented by providing its magnitude and a unit vector along its direction.

Base vectors and vector components:

Base vectors are a set of vectors selected as a base to represent all other vectors. The idea is to construct each vector from the addition of vectors along the base directions. For example, the vector in the figure can be written as the sum of the three vectors u1, u2, and u3, each along the direction of one of the base vectors e1, e2, and e3, so that

Each one of the vectors u1, u2, and u3 is parallel to one of the base vectors and can be written as scalar multiple of that base. Let u 1, u 2, and u 3 denote these scalar multipliers such that one has






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