Orthogonal Vectors Checker

About this calculator

Two vectors are orthogonal (perpendicular, meeting at exactly 90°) precisely when their dot product is zero: for 3D vectors a = (a₁, a₂, a₃) and b = (b₁, b₂, b₃), that's a·b = a₁b₁ + a₂b₂ + a₃b₃. Any nonzero result tells you the angle between them via cosθ = (a·b)/(|a||b|), but zero is the special case that means the vectors share no component in each other's direction.

Engineering, physics, and computer-graphics work leans on this test constantly — resolving forces into independent perpendicular components in statics, checking that a surface normal is perpendicular to a triangle's edges for correct lighting in 3D rendering, or verifying that basis vectors used in a coordinate system are mutually independent — which is why students and developers alike reach for a quick dot-product check rather than computing angles by hand.