Find a unit vector that has the same direction as the given vector. 4i - j + 8k?

Solution:

Vectors that have magnitude equals to 1 are called unit vectors, denoted by ^a. 

The length of unit vectors is 1. Unit vectors are generally used to denote the direction of a vector.

Given, the vector u is 4i - j + 8k

We need to find a unit vector that has the same direction as the given vector.

For the same direction, the sign configuration (+ - +) for the components remains unchanged.

For any vector u, the unit vector in the direction of u is (1/|u|) × u

Where, |u|= √(sum of squares of the magnitudes of the components of u)

|u| = √(4² + (-1)² + 8²)

By further calculation

|u| = √(16 + 1 + 64)

|u| = 9

Therefore, the unit vector of 4i - j + 8k is 1/9 (4i - j + 8k).

Find a unit vector that has the same direction as the given vector. 4i - j + 8k?

Summary:

A unit vector that has the same direction as the given vector 4i - j + 8k is 1/9 (4i - j + 8k).