Vector and Coordinate Calculators
Vector Addition and Subtraction Calculator
Add and subtract vectors, multiply a vector by a number and find a linear combination of vectors from coordinates with a step-by-step solution.
Vector Magnitude Calculator: Length from Coordinates
Find the length (magnitude) of a vector from its coordinates or from two points in 2D and 3D, the unit vector and direction cosines. Exact answer with roots.
Distance from a Point to a Line and a Plane Calculator
Find the distance from a point to a line in 2D and 3D and from a point to a plane, with the foot of the perpendicular and a step-by-step solution.
Midpoint Calculator: Midpoint of a Segment
Find the midpoint of a segment, the point dividing a segment in a given ratio and the endpoint from the midpoint in 2D and 3D.
Cross Product and Triple Product Calculator
Find the cross product via a determinant, the area of a parallelogram and a triangle, the scalar triple product and the volume of a tetrahedron from coordinates.
Dot Product Calculator: Vectors in 2D and 3D
Find the dot product of vectors from coordinates or from lengths and the angle, the cosine of the angle, the projection and a perpendicularity check.
Angle Between Vectors Calculator
Find the angle between two vectors from coordinates in 2D and 3D and the angle of a triangle from three points: exact cosine and the angle in degrees.
Distance Between Two Points Calculator
Find the distance between two points from their coordinates in 2D and 3D with an exact answer and a step-by-step solution.
Equation of a Line Calculator: Two Points, Slope, General Form
Find the equation of a line through two points, from a point and a vector or the slope: general, slope-intercept, symmetric, parametric and intercept forms with a graph.
Equation of a Plane Calculator: Three Points, Normal Vector
Find the equation of a plane through three points, from a point and a normal vector or two direction vectors: general and intercept forms, the normal vector.
Slope Calculator: Slope of a Line Through Two Points
Slope and angle of a line through two points, the equation y = mx + b and percent grade, with the solution.
Circle Equation Calculator: Centre, Radius and General Form
The equation of a circle from its centre and radius or a point, and the centre and radius from the general form.
Angle Between Two Lines Calculator from General Equations
The angle between two lines from their general equations, their relative position and intersection, with a figure.
Two Planes Calculator: Angle, Position and Distance
The angle between two planes, their relative position and the distance between parallel planes.
Triangle from Coordinates Calculator: Medians, Orthocenter, Circle Centers
Area, medians, orthocenter, incenter, circumcenter and the position of a point from the vertex coordinates.
Vector Basis Calculator: Check and Decompose a Vector
Check whether vectors form a basis and decompose a vector in the basis, with the solution.
Vector and coordinate calculators solve analytic geometry problems in the plane and in space: vector operations, dot and cross products, angles, distances, equations of lines and planes. Every solution is shown step by step; coordinates can be fractions, and the answer is exact, with simplified roots.
What you can solve
- Vectors — magnitude, sum and difference, scalar multiplication, dot, cross and triple products, the angle between vectors.
- Points — distance between points, midpoint, dividing a segment in a ratio, the area of a triangle from its vertices.
- Lines and planes — the equation of a line in different forms with a graph, the equation of a plane, the distance from a point to a line and to a plane.
- Slope — Slope and angle of a line through two points, the equation y = mx + b and percent grade, with the solution.