Vectors help pleeeeeeeeeease!?

Vector A points in the negative y direction and has a magnitude of 6 units. Vector B has three times the magnitude and points in the positive x direction. Find the direction and magnitude of the following vectors.





(a) A + B





° (counterclockwise from the +x-axis)


(b) A - B





° (counterclockwise from the +x-axis)


(c) B - A





° (counterclockwise from the +x-axis)

Vectors help pleeeeeeeeeease!?
Just use the pythagorean theorem to get the magnitudes.





The magnitudes are 6 and 18, if I understand your question correctly, and they will all be positive when you square them, so you will have a^2 + b^2 = c^2, or 36 + 324 = c^2,





so c = sqroot360 or 6*sqroot10, or 18.97 approx.





The question now is what direcion.





The tan of the angle will be |y/x|, or 1/3





Thus the angle will be arctan 1/3 (be sure to set you calc to degrees) or 18.435 degrees from the x-axis.





Since in A + B, we have a neg y and a pos x, it will lie in the 4th quadrant, so ithe angle will be 360 - 18.435 degrees: approx 341.565 degrees





Since A-B has a negative y and a negative x, it will lie in the 3rd quadrant, so the angle will be 180 + 18.435, or approx 198.435 degrees.





Sice B - A has both values positive, it is in the 1st quadrant, so it will be 0 + 18.435, or approx 18.435 degrees.





Hope that helps ya!