high School⏱ 3 min

Vector Magnitude

|v| = √(x²+y²)

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x = 3y = 4|v| = 5.00O(3, 4)

Vector coordinates

∣v⃗∣2=x2+y2=32+42=25|\vec{v}|^2 = x^2 + y^2 = 3^2 + 4^2 = 25
∣v⃗∣=32+42=9+16=25=5.0000|\vec{v}| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5.0000

|v| = 5.0000

Magnitude (length) of a vector = distance from origin. Pythagorean theorem: |v|² = x² + y².