If vector times vector equals scalar like

also called: inner product




1 Introduction





With the scalar product, a vector is not multiplied by a scalar, as is the case with scalar multiplication, but instead a vector is multiplied by a vector. The result of this calculation - i.e. the product - is always a scalar. Hence the name scalar product.

The scalar product is used to calculate the angle between two vectors. The formula is extremely useful and widely used, especially when examining positional relationships. They can be used to find out whether vectors, straight lines or planes are perpendicular to one another (i.e. at a 90 ° angle).




2. Formula





Fortunately, the scalar product is very easy to calculate.



Generally:





Example:





Example:







3. Notes





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