How two vectors can be broken down to be rearranged to form scalars.

Question

I am independently studying Ap Physics C: Mechanics and I am learning about dot product. However, I don’t understand how Scalar = A x B = |A| x BII. (Where A and B are vectors, the || represent magnitude, the BII means the component of B parallel to A) I can’t seem to be able to rationalize it and it frustrates me.

Edit: A bit of clarification added

In: 3

Answer 1

Try thinking of it in terms of a concrete example – the standard choice is the amount of work done by an object being displaced with displacement S in a field of force F.

The work done – a scalar, in Joules – is equal to the displacement multiplied by the force in the same direction as that displacement.

So you take the absolute value of the displacement (|S|) and you multiply it by the force parallel to that displacement (FII)

You can safely discard both vectors directional information because you’ve already removed any components that aren’t in the relevant direction, and have reduced the problem to a one-dimensional one.