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Vector operations calculators handle 2D and 3D vector mathematics: addition, subtraction, scalar multiplication, dot product, cross product, and magnitude.

Formula

Cross product: a×b = (a₂b₃−a₃b₂, a₃b₁−a₁b₃, a₁b₂−a₂b₁)

b: (a₂b₃−a₃b₂ — (a₂b₃−a₃b₂

Guida passo passo

1Addition: a + b = (a₁+b₁, a₂+b₂, a₃+b₃)
2Dot product: a·b = a₁b₁+a₂b₂+a₃b₃ (scalar)
3Cross product: a×b = (a₂b₃−a₃b₂, a₃b₁−a₁b₃, a₁b₂−a₂b₁)
4Magnitude: |a| = √(a₁²+a₂²+a₃²)

Esempi risolti

Ingresso

a=(3,1,−2) and b=(1,4,2)

Risultato

Dot product = 3+4−4 = 3; |a| = √14 ≈ 3.74

Domande frequenti

What is Vector Operations?

Vector operations calculators handle 2D and 3D vector mathematics: addition, subtraction, scalar multiplication, dot product, cross product, and magnitude. Use this calculator for accurate, instant results.

How accurate is the Vector Operations calculator?

The calculator uses the standard published formula for vector operations. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

What units does the Vector Operations calculator use?

Enter values in the units shown in each input field. The calculator displays results in standard units and shows the calculation steps.

What formula does the Vector Operations calculator use?

The core formula is: Addition: a + b = (a₁+b₁, a₂+b₂, a₃+b₃). Each step in the calculation is shown so you can verify the result manually.

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