Compute the dot (inner) product of two vectors with geometric interpretation.
The dot product (inner product) of two vectors A and B is the sum of the products of corresponding components: A·B = Σ AᵢBᵢ. Geometrically, A·B = ||A|| ||B|| cos θ where θ is the angle between them. Two vectors are orthogonal (perpendicular) if and only if their dot product is zero.
Algebraic Form
A · B = Σᵢ AᵢBᵢ
Geometric Form
A · B = ||A|| · ||B|| · cos(θ)
When the vectors are perpendicular (orthogonal). This is the standard test for orthogonality in any dimension.
Yes. It is negative when the angle between the vectors exceeds 90°, meaning they point in generally opposite directions.