Question

Find a unit vector u in the direction of v. Verify that ||0|| = 1.v = (4, -3)U =

Answer 1

u = <(4/5), (-3/5)>

Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1

Step-by-step explanation

The unit vector in the direction of any vector is that vector divided by the magnitude of the vector.

u = Unit vector in the direction of v = (vector v)/(magnitude of vector v)

v = <4, -3> = 4i - 3j

Magnitude of v = |v| = √[4² + (-3)²] = √(16 + 9) = √25 = 5

u = (4i - 3j)/5 = (4i/5) - (3j/5)

u = <(4/5), (-3/5)>

Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1

Hope this Helps!!!