Find a unit vector that has the same direction as the given vector. -3i + 7j

Solution:

Given, the vector v is -3i + 7j

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| = √((-3)² + 7² )

|v| = √(9 + 49)

|v| = √58

Therefore, the unit vector is 1/√58 (-3i + 7j).

Find a unit vector that has the same direction as the given vector. -3i + 7j

Summary:

A unit vector that has the same direction as the given vector v = -3i + 7j is 1/√58 (-3i + 7j).