Linear Algebra

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.

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