Question

Find a unit vector u in the direction of v. Verify that ||u|| = 1.
v = <−5, −2>.

Answer 1

To find a unit vector in the direction of v, calculate the magnitude of v and divide v by its magnitude. The unit vector u is (-5 / sqrt(29), -2 / sqrt(29)), and its magnitude is 1.

Step-by-step explanation:

To find a unit vector in the direction of v, we need to calculate the magnitude of v and then divide v by its magnitude.

Let's find the magnitude of v:

|v| = sqrt((-5)^2 + (-2)^2) = sqrt(25 + 4) = sqrt(29).

Now, we divide v by its magnitude to obtain the unit vector:

u = v / |v| = (-5 / sqrt(29), -2 / sqrt(29)).

To verify that ||u|| = 1, we calculate the magnitude of u:

||u|| = sqrt((-5 / sqrt(29))^2 + (-2 / sqrt(29))^2) = sqrt(25/29 + 4/29) = sqrt(29/29) = 1.