Find the dot product of two vectors and the angle between them. Enter both vectors, components separated by commas.
Dot Product
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Scalar result.Usage Tip
Projection, work in physics, and similarity in machine learning all rest on the dot product.
THE MATH
A · B = sum of products of matching components
cos(angle) = (A · B) ÷ (|A| |B|)
cos(angle) = (A · B) ÷ (|A| |B|)
The dot product combines two vectors into a single number, related to how aligned they are.
Zero means perpendicular; positive means a similar direction, negative the opposite.
Zero means perpendicular; positive means a similar direction, negative the opposite.
Enter two vectors of equal length.
The angle between them and both magnitudes are shown.
The dot product is zero exactly when the vectors are perpendicular.
The angle between them and both magnitudes are shown.
The dot product is zero exactly when the vectors are perpendicular.