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| = √(x^2 + y^2)
Substituting the values of x and y from vector u:
|u| = √((-3)^2 + (-3)^2)
= √(9 + 9)
= √18
≈ 4.2
Rounding the magnitude to the nearest tenth, |u| ≈ 4.2.
To find the direction angle θ, we can use the formula:
θ = arctan(y / x)
Substituting the values of x and y from vector u:
θ = arctan((-3) / (-3))
= arctan(1)
≈ 45°
Rounding the direction angle to the nearest degree, θ ≈ 45°.
Therefore, the magnitude of vector u is approximately 4.2 and the direction angle is approximately 45°.
To find the magnitude and direction angle of vector u = (-3, -3), follow these steps:
Step 1: Calculate the magnitude of vector u using the formula:
magnitude (|u|) = √(x^2 + y^2)
where x and y are the components of vector u.
Plugging in the values, we have:
|u| = √((-3)^2 + (-3)^2)
= √(9 + 9)
= √18
Rounding |u| to the nearest tenth, we get: |u| ≈ 4.2
Step 2: Calculate the direction angle θ of vector u using the formula:
θ = tan^(-1)(y / x)
where x and y are the components of vector u.
Plugging in the values, we have:
θ = tan^(-1)(-3 / -3)
= tan^(-1)(1)
≈ 45°
Therefore, the magnitude of vector u is approximately 4.2 and the direction angle is approximately 45°.