Matematika

Kalkulačka vektorových operací

Vector Operations

Vector A

Vector B

What is Vector Operations Calculator?

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Kalkulačky vektorových operací zvládají 2D a 3D vektorovou matematiku: sčítání, odčítání, skalární násobení, bodový součin, křížový součin a velikost.

Calkulon makes complex calculations simple — built for students and everyday problem-solvers.

Vzorec

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f(x)Křížový součin: a×b = (a₂b₃−a₃b₂, a₃b1−a₁b3, a₁b₂−a₂b₁)

Variable Legend

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Symbol	Jméno	Jednotka	Popis
b	(a₂b₃−a₃b₂	—	(a₂b₃−a₃b₂

How to Vector Operations Calculator

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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)

Worked Examples

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Example 1

Given:a=(3,1,−2) and b=(1,4,2)

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

Vector Operations Summary

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Operation	Formula	Result
Addition	(a₁+b₁, a₂+b₂, a₃+b₃)	Vector
Subtraction	(a₁−b₁, a₂−b₂, a₃−b₃)	Vector
Dot product	Σaᵢbᵢ	Scalar
Cross product	Determinant formula	Vector (3D only)
Magnitude	√(Σaᵢ²)	Scalar

Frequently Asked Questions

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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.

References

›Vectors — Khan Academy

Deep Dive

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Formula-verified for precision

Reviewed October 2026

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