Find a unit vector that has the same direction as the given vector. -5i + 7j

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.

The given vector is

-5i + 7j

By using the Pythagorean theorem

|-5i + 7j | = √(-5)² + (7)²

|-5i + 7j | = √(25 + 49)

|-5i + 7j | = √74

So the unit vector is

Unit vector = -5i/√74 + 7i/√74

Therefore, the unit vector is -5i/√74 + 7i/√74.

Find a unit vector that has the same direction as the given vector. -5i + 7j

Summary:

A unit vector that has the same direction as the given vector -5i + 7j is -5i/√74 + 7i/√74.