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Vector Visualizer

Vectors in R² and R³ — addition, scaling, dot and cross products

Two editable vectors with draggable tips. See sum, difference, scalar multiples, dot product, and the angle between them. Toggle to R³ for an oblique projection and watch the cross product emerge as the axis orthogonal to both.

Vector a (purple)

Vector b (gold)

Scalar c

1.5

aba+ba-b
|a| = 3.162
|b| = 2.236
a\u00B7b = 5.000
\u03B8 = 45.00\u00B0
ab=abcosθ\mathbf{a}\cdot\mathbf{b} = \|\mathbf{a}\|\,\|\mathbf{b}\|\cos\theta

Drag the arrow tips. Purple dashed = a+b, red dashed = a-b, faint purple = c\u00B7a.

Vector Visualizer — Linear Algebra Labs · hbar.university