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| = √(x^2 + y^2)

Substituting the values of x and y from vector u:

|u| = √((-3)^2 + (-3)^2)
= √(9 + 9)
= √18
≈ 4.2

Rounding the magnitude to the nearest tenth, |u| ≈ 4.2.

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

θ = arctan(y / x)

Substituting the values of x and y from vector u:

θ = arctan((-3) / (-3))
= arctan(1)
≈ 45°

Rounding the direction angle to the nearest degree, θ ≈ 45°.

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