## Scalar Product

Given two vectors the scalar product, the length of the two vectors and the angle included 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°

### Example 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.