## Scalar Product

Given two vectors the scalar product, the length of the two vectors and the included angle are calculated.

### Example 1:

`
-> ⎧ 1 ⎫ -> ⎧ 5 ⎫
a = ⎪ 3 ⎪ b = ⎪ 0 ⎪
⎩ 1 ⎭ ⎩ 3 ⎭
Scalar product of the vec. = 8
Length of the first vector = 3.32
Length of the second vector = 5.83
included angle α = 65.56° `

Beispiel 2:

`
-> ⎧ 1 ⎫ -> ⎧ 0 ⎫
a = ⎪ 2 ⎪ b = ⎪-3 ⎪
⎩ 3 ⎭ ⎩ 2 ⎭
Scalar product of the vec. = 0
Length of the first vector = 3,7416574
Length of the second vector = 3,6055513
included angle α = 90°`

The scalar product is zero. So the vectors are orthogonal.

### See also:

Wikipedia: Dot product