Vector Magnitude and Direction Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

easy
Find ∥⟨−5,12⟩∥\|\langle -5, 12 \rangle\|.

Solution

  1. 1
    (−5)2+122=25+144=169=13\sqrt{(-5)^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13.
  2. 2
    This is a 5-12-13 Pythagorean triple.

Answer

1313
Magnitude is always non-negative regardless of the signs of the components. The formula uses squares, so negative components don't affect the result.

About Vector Magnitude and Direction

The magnitude ∥v∥\|\mathbf{v}\| is a vector's length; the direction is the angle it makes with a reference axis.

Learn more about Vector Magnitude and Direction →

More Vector Magnitude and Direction Examples

Example 1 easy

Find the magnitude of [formula].

Example 2 medium

Find the unit vector in the direction of [formula].

Example 3 medium

Find the magnitude and direction angle of the vector v = <3, 4>.

Example 5 hard

Find the direction angle [formula] of [formula] measured from the positive [formula]-axis.

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