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)
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.
To find the magnitude and direction angle of vector u = (9, -2), we can use the following formulas:
1. Magnitude (|u|) = √(x^2 + y^2)
2. Direction angle (θ) = tan^(-1)(y / x)
Given that u = (9, -2), we can substitute the values into the formulas:
1. |u| = √(9^2 + (-2)^2)
= √(81 + 4)
= √85
≈ 9.2 (rounded to the nearest tenth)
2. θ = tan^(-1)(-2 / 9)
≈ -12.4° (rounded to the nearest degree)
Therefore, the magnitude of vector u is approximately 9.2 and the direction angle is approximately -12.4°.