Question

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.
u = (9, -2)

Answer 1

To find the magnitude of the vector u, we use the formula:
|magnitude| = √(x^2 + y^2)

Plugging in the values x = 9 and y = -2, we get:
|magnitude| = √(9^2 + (-2)^2)
|magnitude| = √(81 + 4)
|magnitude| = √85
Magnitude ≈ 9.2

To find the direction angle θ, we use the formula:
θ = atan(y/x)

Plugging in the values x = 9 and y = -2, we get:
θ = atan((-2)/9)
θ ≈ -0.218 radians

To convert radians to degrees, we multiply by 180/π:
θ ≈ -0.218 * (180/π)
θ ≈ -12.5 degrees

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