Question

Find the unit vector u with the same direction as v =⟨9, – 4⟩

Answer 1

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 )