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 vector u, we use the formula:
|u| = sqrt((x^2) + (y^2)), where x and y are the components of vector u.
Given that u = (9, -2), we can substitute the values into the formula:
|u| = sqrt((9^2) + (-2^2)) = sqrt(81 + 4) = sqrt(85) ≈ 9.2
Therefore, the magnitude of vector u is approximately 9.2.
To find the direction angle θ, we use the formula:
θ = tan^(-1)(y/x), where x and y are the components of vector u.
Substituting the values of u = (9, -2) into the formula, we get:
θ = tan^(-1)(-2/9) ≈ -12.2°
Therefore, the direction angle of vector u is approximately -12.2°.
To find the magnitude and direction angle of vector u = (9, -2), we can use the following formulas:
Magnitude:
The magnitude of a vector u = (x, y) is given by the formula:
||u|| = √(x^2 + y^2)
Direction Angle:
The direction angle θ of a vector u = (x, y) is given by the formula:
θ = tan^(-1)(y / x)
Let's calculate the magnitude and direction angle of vector u:
Magnitude:
||u|| = √(9^2 + (-2)^2)
= √(81 + 4)
= √85
≈ 9.2 (rounded to the nearest tenth)
Direction Angle:
θ = tan^(-1)(-2 / 9)
≈ -12.5 degrees (rounded to the nearest degree)
Therefore, the magnitude of vector u is 9.2 and the direction angle is approximately -12.5 degrees.