Find the magnitude and direction angle θ of the following vectors. Round the magnitude to the nearest tenth, and round the direction angle to the nearest degree, if rounding is necessary.

Question

u = (-3, -3)

Answer 1

To find the magnitude of vector u, we can use the formula:

|u| = sqrt((-3)^2 + (-3)^2)

|u| = sqrt(9 + 9)

|u| = sqrt(18)

|u| ≈ 4.2

To find the direction angle θ of vector u, we can use the formula:

θ = arctan(-3/-3)

θ = arctan(1)

θ ≈ 45 degrees

Therefore, the magnitude of vector u is approximately 4.2 and the direction angle θ is approximately 45 degrees.