Calculate the scalar dot product of two vectors in 2D or 3D space.
Space Dimension
Vector A Components
Vector B Components
Vector Scaler
32
A · B
Angle between (θ)12.93°
OrthogonalityNo
Dot Product TypePositive (Acute)
What is Dot Product?
The dot product is an algebraic operation that takes two equal-length sequences of numbers and returns a single number. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them.
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Pro Tips
If the dot product is 0, the vectors are orthogonal (perpendicular).
If the dot product is positive, the angle is acute; if negative, the angle is obtuse.
A · B = |A| |B| cos(θ).
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Fun Facts
"The dot product is used in graphics programming to calculate lighting and shading."
"It measures how much of one vector is in the direction of another."
"In physics, work is the dot product of the force and displacement vectors."
