Visualise planes in 3D geometry in 3D

Direct answer

Change a, b, c and d to see how a plane tilts and moves, with its normal, foot of perpendicular and distance from the origin.

The plane ax + by + cz = d has normal (a, b, c). Changing d slides the plane along its normal without tilting it.

Simulation

3D geometry

a 1

b 2

c 2

d 6

Drag to rotate, two fingers or right-drag to pan, scroll or pinch to zoom. The toolbar has views, cutaway, measure and “show the maths”.

What's happening? The plane ax + by + cz = d has normal (a, b, c). Changing d slides the plane along its normal without tilting it.

Learn more

Where it is in NCERT: Class 12 Mathematics Part II, “Three Dimensional Geometry” (Direction Cosines and Direction Ratios of a Line, Equation of a Line in Space, Angle between Two Lines, Shortest Distance between Two Lines) · ncert.nic.in
Topic notes and formulas: Three Dimensional Geometry
Printable formula sheet
Chapter-wise JEE Main PYQs (17)