If a vector K has component Kx = 4.1 and Ky = -13, then find the magnitude K and direction (as a positive rotation angle relative to the +x axis) of the vector.
Kmag=sqrt(4.1^2 +(-13)^2)
I don't have a clue what "positive" rotation means. If you mean clockwise as positive, then
Theta=arctan13/4.1
If you mean counterclockwise rotation as "positive", then
theta= 360deg - aboveangle
To find the magnitude and direction of a vector with given components, you can use the Pythagorean theorem and trigonometric functions.
1. Magnitude (|K|):
The magnitude of a vector K can be calculated using the Pythagorean theorem:
|K| = sqrt(Kx^2 + Ky^2)
In this case, the given components are Kx = 4.1 and Ky = -13. Plugging these values into the formula:
|K| = sqrt((4.1)^2 + (-13)^2)
= sqrt(16.81 + 169)
= sqrt(185.81)
≈ 13.62
So, the magnitude of vector K is approximately 13.62.
2. Direction (θ):
To find the direction of the vector as a positive rotation angle relative to the +x axis, you can use the inverse tangent function (arctan or tan^(-1)).
θ = arctan(Ky / Kx)
Plugging in the given values:
θ = arctan((-13) / 4.1)
≈ arctan(-3.17)
≈ -73.81°
The negative sign indicates that the direction is measured in the opposite direction from the positive x-axis. To obtain the positive rotation angle:
θ = 360° - 73.81°
≈ 286.19°
Therefore, the direction of the vector K relative to the +x axis is approximately 286.19°.