To find a unit vector in the direction of a given vector, we first need to determine the magnitude of the given vector. The given vector v = (1, 3).
The magnitude of a vector v = (x, y) is calculated using the formula:
|v| = √(x² + y²)
For our vector v:
|v| = √(1² + 3²) = √(1 + 9) = √10
Now, to find the unit vector u in the direction of v, we divide each component of the vector v by its magnitude:
u = (1/√10, 3/√10)
This gives us the unit vector:
u ≈ (0.316, 0.948)
Thus, the unit vector in the direction of the given vector v = (1, 3) is approximately (0.316, 0.948).