How do I find a unit vector in the same direction as the vector 3i + 7j?

To find a unit vector that has the same direction as the vector 3i + 7j, we can follow these steps:

Step 1: Identify the vector components – The vector can be expressed as v = (3, 7), where its components are 3 and 7.
Step 2: Calculate the magnitude of the vector – The magnitude |v| can be calculated using the formula:

|v| = √(x² + y²) = √(3² + 7²) = √(9 + 49) = √58

Step 3: Divide each component by the magnitude – To get the unit vector u in the same direction:

u = (1/|v|) * v = (1/√58) * (3, 7) = (3/√58, 7/√58)

u = (3/√58)i + (7/√58)j

This unit vector u has the same direction as the original vector 3i + 7j, but its magnitude is 1.