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 = (-12, 2)
To find the magnitude of the vector u = (-12, 2), we use the formula for magnitude:
|u| = √(x^2 + y^2)
where x and y are the components of the vector.
|u| = √((-12)^2 + 2^2)
|u| = √(144 + 4)
|u| = √148
|u| ≈ 12.1
Rounding to the nearest tenth, the magnitude of u is approximately 12.1.
To find the direction angle θ, we use the formula:
θ = arctan(y / x)
where x and y are the components of the vector.
θ = arctan(2 / -12)
θ ≈ -9.5°
Rounding to the nearest degree, the direction angle θ of vector u is approximately -9°.
To find the magnitude of vector u, we can use the formula:
Magnitude of a vector = sqrt(x^2 + y^2)
where x and y are the components of the vector.
Plugging in the values for vector u, we have:
Magnitude of u = sqrt((-12)^2 + 2^2)
= sqrt(144 + 4)
= sqrt(148)
≈ 12.2 (rounded to the nearest tenth)
To find the direction angle θ, we can use the formula:
θ = arctan(y/x)
Plugging in the values for vector u, we have:
θ = arctan(2/(-12))
≈ arctan(-0.1667)
≈ -9.5 degrees (rounded to the nearest degree)
Therefore, the magnitude of vector u is approximately 12.2, and the direction angle θ is approximately -9.5 degrees.