You get other vectors, usually perpendicular to each other, that - when added together - result in the original vector. These component vectors are usually along the axes of some selected coordinate system.
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If they are parallel, you can add them algebraically to get a resultant vector. Then you can resolve the resultant vector to obtain the vector components.
A dot product is a scalar product so it is a single number with only one component. A cross product or vector product is a vector which has three components like the original vectors.
Consider two vectors A and B Represented by directionel lines OM and ON respectivelynow add the two vectors by head to tail tail of vector addition now resolve it into rectangular components as shown in figure
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.
The zero vector is both parallel and perpendicular to any other vector. V.0 = 0 means zero vector is perpendicular to V and Vx0 = 0 means zero vector is parallel to V.