Final answer:
To find the unit vector u with the same direction as v = ⟨9, -4⟩, calculate the magnitude of v, |v| = sqrt(97), and then divide each component of v by its magnitude to obtain u.
Step-by-step explanation:
To find the unit vector u with the same direction as v = ⟨9, – 4), we first calculate the magnitude of vector v and then divide each of its components by this magnitude.
The magnitude of vector v, denoted as |v|, is calculated using the formula:
|v| = √(9² + (-4)²)
= √(81 + 16)
= √97
= approximately 9.849
Now, we divide each component of v by |v| to get the unit vector u:
u = ⟨ 9 / 9.849, -4 / 9.849 )