The following formula is used to calculate a vector length:
\[ |u| = \sqrt{x^2 + y^2 + z^2} \]
A vector length is equivalent to a vector magnitude and is equal to the square root of the sum of the squares of each vector unit.
Let's say we have a vector with coordinates (3, 4, 5). To find the length of this vector, we can use the formula:
\[ |u| = \sqrt{3^2 + 4^2 + 5^2} \]
Calculating the values:
\[ |u| = \sqrt{9 + 16 + 25} = \sqrt{50} \approx 7.07 \]
Therefore, the length of the vector (3, 4, 5) is approximately 7.07 units.
