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Quaternions were invented by Sir William Hamilton as a mathematical method of dealing with directions in space without the use of the arbitrary axes of Cartesian geometry. A quaternion itself is the factor or operator which changes one directed line (or vector) into another. Quantities which do not include direction are known as scalar, and any vector can be regarded as the product of unit vector (which gives the direction) and a scalar quantity. If a vector be rotated into a new direction, the operator is known as a versor, and therefore this versor must imply the existence of an axis and a definite angle.

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