Acharge 4q is at the origin, and a charge of -3q is on the positive x-axis at x = a. where would you place a third charge so it would experience zero net electric force? (note: either enter your answer as an unevaluated expression, e. g., (3/2 + sqrt(3))a, or if evaluated, use 2 decimal places.) your expression should be in terms of the given variable.

6.45 a

Explanation:

Charge on O, q1 = 4q

Charge on A, q2 = - 3 q

OA = a

Let the net force is zero at point P, where AP = x , let a charge Q is placed at P.

The force on point P due to the charge q1 = The force on point P due to the  

                                                                          charge q2

By using Coulomb's law

a + x = 1.155 x

0.155 x = a

x = 6.45 a

Thus, the force is zero at x = 6.45 a.

the total distance traveled by the car is

30km + 49km = 79 km .

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west