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Online algebra calculator that allows you to calculate the Product of three dimensional vectors with the given vector coordinates.

The dot product is a very important operation in graphics programming. The interesting thing about it is that the result is not a vector but a single number (a scalar). It can be used to find the angle between two vectors. The dot product is defined as:

A · B = |A| * |B| * cos(A,B)

The dot product is the length of vector A, multiplied by the length of vector B, multiplied by the cosine of the angle between A and B. Because in shader programming we usually don't know the angle between A and B, this is of little use to us. Fortunately, there is another way to calculate the dot product:

A · B = Ax * Bx + Ay * By + Az * Bz

The dot product is the same as the sum of all vector components multiplied with each other. To find the angle between A and B, we simply divide this value by the product of |A| and |B|. In the case of normalized vectors the dot product is equal to the cosine of the angle between A and B because |A| and |B| are both 1.