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 = (9, -2)

Answer 1

The magnitude of vector u is given by the formula:

|u| = sqrt(9^2 + (-2)^2) = sqrt(81 + 4) = sqrt(85) ≈ 9.2

The direction angle θ of vector u is given by the formula:

θ = arctan(-2/9)

Using a calculator, we find arctan(-2/9) ≈ -0.218 radians ≈ -12.5 degrees

Therefore, the magnitude of vector u is approximately 9.2 and the direction angle θ is approximately -12.5 degrees.