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 = (-3, -3)
To find the magnitude of vector u, we can use the formula:
|u| = sqrt((-3)^2 + (-3)^2)
|u| = sqrt(9 + 9)
|u| = sqrt(18)
|u| ≈ 4.2
To find the direction angle θ of vector u, we can use the formula:
θ = arctan(-3/-3)
θ = arctan(1)
θ ≈ 45 degrees
Therefore, the magnitude of vector u is approximately 4.2 and the direction angle θ is approximately 45 degrees.
To find the magnitude and direction angle of vector u = (-3, -3), we can use the formulas:
Magnitude (|u|) = √(x² + y²)
Direction angle (θ) = tan⁻¹(y / x)
Let's calculate the magnitude first:
Magnitude (|u|) = √((-3)² + (-3)²)
= √(9 + 9)
= √18
≈ 4.2 (rounded to the nearest tenth)
Now let's calculate the direction angle:
Direction angle (θ) = tan⁻¹((-3) / (-3))
= tan⁻¹(1)
≈ 45° (rounded to the nearest degree)
Therefore, the magnitude of vector u is approximately 4.2 and the direction angle θ is approximately 45 degrees.