Magnitude of a Vector

About The magnitude of a Vector

The magnitude of a vector formula aids in the summarization of a vector's numerical value. A vector has a magnitude and a direction. This magnitude of a vector formula summarises the separate measures of the vector along the x-axis, y-axis, and z-axis. |v| stands for it. A vector's magnitude must always be a positive number or zero, and it cannot be negative. Let's look at a few solved cases to help us comprehend the magnitude of a vector formula.

What is the Magnitude of a Vector?

The length of a vector A is its magnitude, which is denoted by |A|. The square root of the sum of squares of the vector's components. The magnitude of a vector having direction ratios along the x, y, and z axes is equal to the square root of the sum of the squares of the vector's direction ratios. The magnitude of a vector formula below can plainly demonstrate this.

The magnitude of a Vector Formula

  • For a vector A = x1 i + y1 j + z1 k, its magnitude is: |A| =√(x12 + y12 + z12)
  • For a vector v when one of its endpoints is at origin (0,0) and the other endpoint is at (x, y), its magnitude is: |v| =√(x2 + y2)
  • For a vector v with endpoints at (x1, y1) and (x2, y2), its magnitude is: |v| =√((x2 - x1)2 + (y2 - y1)2)

How to Find Magnitude of a Vector?

To determine the magnitude of a 2-dimensional vector from its coordinates,

Magnitude of a Vector1

Thus,

  • the formula to determine the magnitude of a vector (in two dimensional space) v = (x, y) is: |v| =√(x2 + y2). This formula is derived from the Pythagorean theorem.
  • the formula to determine the magnitude of a vector (in three dimensional space) V = (x, y, z) is: |V| =&Sqrt(x2 + y2 + z2)

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Magnitude of a Vector
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