for v= 4i - 5j, find unit vector u in the direction of v, and write your answer as a linear combination of the standard unit vectors i and j.
To find the unit vector in the direction of v, we first need to find the magnitude of v.
The magnitude of v is given by:
|v| = sqrt((4)^2 + (-5)^2)
|v| = sqrt(16 + 25)
|v| = sqrt(41)
Now, to find the unit vector u in the direction of v, we divide each component of v by its magnitude:
u = (4/sqrt(41))i - (5/sqrt(41))j
Therefore, the unit vector u in the direction of v can be written as:
u = (4/sqrt(41))i - (5/sqrt(41))j