*23*

A

**unit vector**is a vector that has a length of 1. For any given vector, it’s possible to find the unit vector that has the same direction as the given vector.For example, suppose a given vector

**a**= (2, 5, -9). To find the unit vector, we first find the magnitude of vector**a**, which can be found using the formula:Magnitude of vector

**a**= √(2^{2}+5^{2}+ -9^{2}) = 10.488.Next, we divide each of the original vector’s components by the magnitude:

x = 2 / 10.488 = .191

y = 5 / 10.488 = .477

x = -9 / 10.488 = -.858

Thus, the unit vector = (.191, .477, -.858), which has a length of 1 and is along the same direction as the original vector.

To find the unit vector for a given vector, simply enter the coordinates of the original vector below and then click the “Calculate” button.

**Explanation:**

Magnitude of original vector = √(2

^{2}+5^{2}+-9^{2}) = 10.48808848x = 2 / 10.48808848 = 0.19069252

y = 5 / 10.48808848 = 0.47673129

z = -9 / 10.48808848 = -0.85811633

Unit vector = (0.19069252, 0.47673129, -0.85811633)