Two vectors are orthogonal if the angle between them is 90 degrees. Thus, using (**) we see that the dot product of two orthogonal vectors is zero. Conversely, the only way the dot product can be zero is if the angle between the two vectors is 90 degrees (or trivially if one or both of the vectors is the zero vector).

Answer: The dot product can be any real value, including negative and zero. The dot product is 0 only if the vectors are orthogonal (form a right angle).

A positive dot product means that two signals have a lot in common—they are related in a way very similar to two vectors pointing in the same direction. Likewise, a negative dot product means that the signals are related in a negative way, much like vectors pointing in opposing directions.

If A and B are perpendicular (at 90 degrees to each other), the result of the dot product will be zero, because cos(Θ) will be zero. If the angle between A and B are greater than 90 degrees, the dot product will be negative (less than zero), as cos(Θ) will be negative, and the vector lengths are always positive values.

Then the dot product of u with v is u · v = u1v1 + u2v2 + ··· + unvn. Notice that the dot product of two vectors is a scalar, and also that u and v must have the same number of components in order for u · v to be defined.

The dot product of a vector with itself is the square of its magnitude. The dot product of two vectors is commutative; that is, the order of the vectors in the product does not matter. Multiplying a vector by a constant multiplies its dot product with any other vector by the same constant.

Dot product – also known as the “scalar product”, an operation that takes two vectors and returns a scalar quantity. The dot product of two vectors can be defined as the product of the magnitudes of the two vectors and the cosine of the angle between the two vectors.