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Turn one arrow and watch its shadow and the parallelogram change.
Two arrows from the same point: A (blue) along the x-axis and B (rose) at an angle θ. In dot-product mode, B casts a shadow onto A; the dot product A·B is A's length times that shadow, |A||B|cos θ: biggest when the arrows line up, zero at right angles, negative when they point apart. In cross-product mode the two arrows span a shaded parallelogram; the size of the cross product A×B is its area, |A||B|sin θ, and its direction is into or out of the screen, shown by a cross or a dot. Set both lengths and the angle.
Dot and cross products
InteractiveProduct
The math, with your numbers
Work is a dot product: W = F·d. Only the part of the force along the motion does work.
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Want to know why it behaves like this?
The lesson “Multiplying Vectors: Dot & Cross” explains it step by step: What could it even mean to multiply two arrows?