Find the unit vector in the direction of u = (-3,2).
a. u = -3√13 / 13i + 2√13 / 13j
b. u = -3√5 / 5i + 2√5 / 5j
c. u = 3√5 / 5i - 2√5 / 5j
d. u = 3√13 / 13i + 2√13 / 13j
To find the unit vector in the direction of u = (-3,2), we first need to find the magnitude of vector u:
|u| = sqrt((-3)^2 + 2^2)
|u| = sqrt(9 + 4)
|u| = sqrt(13)
Now, the unit vector in the direction of u is given by dividing each component of u by the magnitude of u:
u_unit = (-3/sqrt(13), 2/sqrt(13))
Simplifying this gives:
u_unit = -3√13 / 13i + 2√13 / 13j
Therefore, the correct answer is:
a. u = -3√13 / 13i + 2√13 / 13j