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)
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.
To find the magnitude and direction angle of vector u = (9, -2), we can use the following formulas:
Magnitude (|u|) = √(x^2 + y^2)
Direction angle (θ) = arctan(y / x)
Let's calculate the magnitude first:
|u| = √(9^2 + (-2)^2)
|u| = √(81 + 4)
|u| = √85
|u| ≈ 9.2 (rounded to the nearest tenth)
Now let's calculate the direction angle:
θ = arctan((-2) / 9)
θ ≈ -0.22 radians
To convert the direction angle to degrees, we can use the formula:
θ_degrees = θ * (180 / π)
θ_degrees ≈ -12.6 degrees (rounded to the nearest degree)
Therefore, the magnitude of vector u is approximately 9.2 and the direction angle is approximately -12.6 degrees.