why is The sum of two vectors has the smallest magnitude when the angle between these two vectors is 180t

  C = A - B

Explanation:

The addition of vectors takes into account the magnitude of each vector and its direction, so when adding two vectors, the result depends on the direction of the vectors.

* If the vectors have the same direction the result is maximum

            C = A + A

* if the vectors have 90 between them, the magnitude of the result is given by the Pythagorean Theorem

            C = √(A² + B²)

* if the vectors have 180º between them the result is minimal

            C = A - B

We can also perform this sum graphically, where the resulting vector goes from the origin of the first vector to the tip of the last one, it can clearly be seen that when the vectors are antiparallel (180º angle) the magnitude is minimal