6. Find the MAGNITUDE and ANGLE (counter-clockwise, from q=00, on the x-axis) of the vector C = A + B.

Magnitude of C=

Angle=arctan(Ay+By/Ax+Bx)

Explanation:

Let

A = Axi + Ayj

B = Bxi + Byj

where i and j  are unit vectors in the direction of x and y axes respectively.

C=A+B

C = (Ax + Bx)i + (Ay + By)j

The magnitude of vector C can be calculated by adding the square of  magnitude of its componets and then taking sqaure root.

Magnitude of C=

And the angle will be

Angle=arctan(Ay+By/Ax+Bx)

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach