If the components of a vector are Fx = −2.00 N and Fy = 13.0 N, what are its magnitude and direction?Magnitude: Direction (specify as an angle measured counterclockwise from the positive x axis):

The magnitude and direction of a vector can be found using the components of the vector.

Step 1: Calculate the magnitude of the vector. The magnitude (or length) of a vector can be found using the Pythagorean theorem, which in this context is written as:

F = sqrt((Fx)^2 + (Fy)^2)

Substituting the given values:

F = sqrt((-2.00 N)^2 + (13.0 N)^2) F = sqrt((4 N^2) + (169 N^2)) F = sqrt(173 N^2) F = 13.15 N

So, the magnitude of the vector is 13.15 N.

Step 2: Calculate the direction of the vector. The direction (or angle) of a vector can be found using the tangent function, which in this context is written as:

θ = arctan(Fy / Fx)

Substituting the given values:

θ = arctan(13.0 N / -2.00 N) θ = -80.54 degrees

However, because the angle is measured counterclockwise from the positive x-axis, and the x-component of the vector is negative (indicating a direction to the left of the positive x-axis), we add 180 degrees to this result:

θ = -80.54 degrees + 180 degrees θ = 99.46 degrees

So, the direction of the vector is 99.46 degrees counterclockwise from the positive x-axis.