Equation of a Plane Calculator
Omni Calculator’s equation of a plane calculator will quickly tell you the equation of a plane starting from a vector and a point or three points.
|a|5
|b|3
a · b (dot product)11
Angle between42.833428°
a + b(4, 6, 2)
a − b(2, 2, -2)
Unit vector of a(0.6, 0.8, 0)
a × b (cross product)(8, -6, 2)magnitude 10.198039 — the area of the parallelogram
Projection of a onto b(1.222222, 2.444444, 2.444444)scalar component 3.666667
The formula
magnitude, direction, dot and cross products
Dot and cross do different jobs
The dot product gives a scalar and measures how much two vectors point the same way: zero means perpendicular, positive means acute, negative means obtuse. It is what you use for work, projections and similarity.
The cross product (3D only) gives a vector perpendicular to both, whose magnitude is the area of the parallelogram they span. It is what you use for torque, normals and rotational quantities.