Vector Definitions

Definitions

A Vector is an object that has a three properties: a magnitude (length), a direction, and an angle.

Vector Components are smaller vectors that help split an angled vector towards the coordinate axes in a two and three dimensional coordinate system.

The Magnitude of a vector is the numerical value length that a vector possesses. It is always a positive scalar regardless of direction or angle.

A Unit Vector is vector with a magnitude (length) of 1.

Vector Scaling is the change of a vector's length by a scale factor. Vector Scaling is in other words vector multiplication and division, however these two mathematical operations are combined by the word scaling since if you divide a number by two, that is the same as multiplying a number by one half. Vector Scaling therefore expands or shrinks a vector's length, keeping its angle or inverting it, however.

Vector Addition involves calculating the sum of vectors. This is done by adding together the vector components of each individual vector and once the result is obtained, those components are now the components of the new vector that is equal to the sum of the vectors.

Vector Subtraction involves calculating the difference of vectors. This is done by subtracting the vector components of each individual vector and once the result is obtained, those components are now the components of the new vector that is equal to the difference of the vectors.

The Dot Product of two vectors is one of two methods of vector multiplication, the other is the cross product. A Dot Product is denoted by the multiplication sign (⋅) between two vectors. The Dot Product of two vectors is a scalar quantity of the two vector's components multiplied individually based on their axes and then summed together. It is worth noting that the Dot Product of two vectors is also known as a scalar product as the resultant of the Dot Product of vectors is a scalar quantity.

The Cross Product of two vectors is one of two methods of vector multiplication, the other is the Dot Product. A Cross Product is denoted by the multiplication sign (x) between two vectors. The Cross Product of two vectors is a third vector that not only is perpendicular to the two original vectors, but its magnitude (length) is given by the area of the parallelogram between them and its direction can be determined by the right-hand thumb rule. It is worth noting that the Cross Product of two vectors is also known as a vector product as the resultant of the Cross Product of vectors is a vector quantity.

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