Dot product
Dot product is an interactive experiment in Vectors, a free simulation from StudyFi Lab that runs right in your browser.
The dot product is a number: a·b = a₁b₁ + a₂b₂ + a₃b₃ = |a|·|b|·cos φ. It is positive when the vectors form an acute angle, zero at a right angle and negative at an obtuse one, so a·b = 0 means the vectors are perpendicular. The projection of b onto the direction of a has length a·b / |a|.
Try this: Set a = (4, 1) and look for a b with a·b = 0. Can you find (−1, 4)? Always guess the sign first.
Frequently asked questions
What does the “Dot product” experiment show?
The dot product is a number: a·b = a₁b₁ + a₂b₂ + a₃b₃ = |a|·|b|·cos φ. It is positive when the vectors form an acute angle, zero at a right angle and negative at an obtuse one, so a·b = 0 means the vectors are perpendicular. The projection of b onto the direction of a has length a·b / |a|.
How do I try “Dot product”?
Set a = (4, 1) and look for a b with a·b = 0. Can you find (−1, 4)? Always guess the sign first.
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