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Septim said:… the author derives uses the expression you see on the attachment to convert the abstract form of the dot product into the component form. My question is that how can he relate cosines with directional cosines.
Directional cosines are values used to describe the direction of a vector in three-dimensional space. They are calculated from the angles between the vector and the three axes (x, y, and z) of the coordinate system.
Directional cosines are usually represented using the Greek letter lambda (λ). There are three directional cosines, λx, λy, and λz, which correspond to the x, y, and z axes, respectively.
The directional cosines of a vector can be used to calculate the corresponding unit vector, which has a magnitude of 1 and points in the same direction as the original vector. The unit vector is calculated by dividing the vector's components by its magnitude.
The angle between two vectors can be calculated using the dot product formula, which involves the directional cosines of the two vectors. The dot product of two vectors is equal to the product of their magnitudes and the cosine of the angle between them.
Directional cosines can also be used in higher dimensions, but they are most commonly used in three-dimensional space. In higher dimensions, there would be additional directional cosines for each axis added.