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.
v = (-5, -2)
To find the magnitude of vector v, we can use the formula:
|v| = √(x^2 + y^2)
Where x and y are the components of the vector.
For v = (-5, -2), we have:
|v| = √((-5)^2 + (-2)^2)
= √(25 + 4)
= √29
≈ 5.4
So, the magnitude of v is approximately 5.4.
To find the direction angle θ of vector v, we can use the formula:
θ = tan^(-1)(y/x)
For v = (-5, -2), we have:
θ = tan^(-1)(-2/-5)
≈ tan^(-1)(0.4)
≈ 21 degrees
So, the direction angle θ of vector v is approximately 21 degrees.
To find the magnitude of vector v, you can use the Pythagorean theorem:
magnitude of v = √((-5)^2 + (-2)^2)
= √(25 + 4)
= √29
≈ 5.4 (rounded to the nearest tenth)
To find the direction angle θ, you can use inverse trigonometric functions:
θ = tan^(-1)(-2 / -5)
= tan^(-1)(0.4)
≈ 21.8° (rounded to the nearest degree)
Therefore, the magnitude of vector v is approximately 5.4 and the direction angle θ is approximately 21.8°.