To obtain the position vector in component form from polar coordinates, you can use trigonometric relationships. Given the polar coordinates (r, θ), where r is the radial distance and θ is the angle counterclockwise from the +x axis, you can use the following equations to find the position vector (x, y) in component form:
x = r * cos(θ)
y = r * sin(θ)
In your case, the polar coordinates are (r = 12 m, θ = 160° counterclockwise from the +x axis).
Let's calculate the position vector (x, y):
x = 12 m * cos(160°)
x = 12 m * (-0.866) (cos(160°) is approximately -0.866)
x ≈ -10.392 m
y = 12 m * sin(160°)
y = 12 m * 0.5 (sin(160°) is approximately 0.5)
y = 6 m
So, the position vector in component form is approximately (-10.392 m, 6 m).