the subspace
W through the origin (its spanning vectors are drawn solid blue).
the affine plane
v₀ + W, parallel to W and passing through the tip of
v₀.
Drag the ● tip or edit the boxes to move v₀.
Only the part of v₀ perpendicular to W shifts the plane — moving v₀
along W (gray dashed = the in-W part) gives the same affine plane.
Drag the background to orbit · scroll to zoom · axes labelled x, y, z.