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Why do we say that the vector always contains a scalar?
because vector has a scalar characteristic known as magnitude associated with it
\(\vec v = |\vec v|\hat v\) this explains a lot. the vector is simply a lot of it's unit vectors added together. As 1+1+1+1=4 and 1*4 =4 is the same, we say that the vector is a product of it's scalar component and the unit direction.