Find a unit vector that has the same direction as the given vector. -5i + 9j

Solution:

Given, the vector v is -5i + 9j

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 v, the unit vector in the direction of v is (1/|v|) × v

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

|v| = √((-5)² + 9²)

|v| = √(25 + 81)

|v| = √106

Therefore, the unit vector is 1/√106 (-5i + 9j).

Find a unit vector that has the same direction as the given vector. -5i + 9j

Summary:

A unit vector that has the same direction as the given vector v = -5i + 9j is 1/√106 (-5i + 9j).