Perform vector operations: addition, subtraction, dot product, cross product, and magnitude in 2D or 3D.
| Operation | Formula | Result Type |
|---|---|---|
| Addition | (a1+b1, a2+b2, a3+b3) | Vector |
| Subtraction | (a1-b1, a2-b2, a3-b3) | Vector |
| Dot Product | a1b1 + a2b2 + a3b3 | Scalar |
| Cross Product | (a2b3-a3b2, a3b1-a1b3, a1b2-a2b1) | Vector |
| Magnitude | √(x²+y²+z²) | Scalar |
The dot product measures how parallel two vectors are. It equals |A||B|cosθ. A dot product of zero means the vectors are perpendicular.
Cross product gives a vector perpendicular to both inputs. Used in physics (torque, angular momentum) and 3D graphics (surface normals).
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Open →Enter two vectors (2D or 3D components). The calculator performs addition, subtraction, dot product, cross product, magnitude, and unit vector calculations.
Magnitude: |v| = √(x² + y² + z²). Dot product: a·b = axbx + ayby + azbz. Cross product: a×b = (aybz – azby, azbx – axbz, axby – aybx).
a = (3,4), b = (1,2). a+b = (4,6). |a| = 5. a·b = 3+8 = 11. Angle = cos⁻¹(11/(5×√5)) = 10.3°.
Dot product = 0 means vectors are perpendicular. Cross product gives a vector perpendicular to both inputs (right-hand rule). Normalize to unit vectors before comparing directions.