Question

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)

Answer 1

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.