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)

1 answer

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

|u| = sqrt((x^2) + (y^2)), where x and y are the components of vector u.

Given that u = (9, -2), we can substitute the values into the formula:

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

Therefore, the magnitude of vector u is approximately 9.2.

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

θ = tan^(-1)(y/x), where x and y are the components of vector u.

Substituting the values of u = (9, -2) into the formula, we get:

θ = tan^(-1)(-2/9) ≈ -12.2°

Therefore, the direction angle of vector u is approximately -12.2°.