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Parametric, Polar & Vectors · Vector Operations

Vector Magnitude

∣v⃗∣=v12+v22+v32|\vec{v}| = \sqrt{v_1^2 + v_2^2 + v_3^2}

The magnitude (length) of a vector v = ⟨v₁, v₂, v₃⟩.

  • 3 variables
  • 2 worked examples
  • 12 in Parametric, Polar & Vectors

Variables

Variables used in the Vector Magnitude formula
SymbolNameUnit
v1x-component -
v2y-component -
v3z-component -

Worked examples

Find |⟨3, 4⟩|.
  1. √(9 + 16) = √25 = 5

Answer: 5

1 more worked examplePremium

Find |⟨1, 2, 2⟩|.

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Common questions

What is the Vector Magnitude?

The magnitude (length) of a vector v = ⟨v₁, v₂, v₃⟩. It is one of the parametric, polar & vectors formulas in the CalcRef reference.

What do the symbols in the Vector Magnitude mean?

In the Vector Magnitude, v1 is the x-component; v2 is the y-component; v3 is the z-component.

How do you use the Vector Magnitude?

Worked example. Find |⟨3, 4⟩|. √(9 + 16) = √25 = 5. Answer: 5.

Practice

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