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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:

def trilaterate_v(self, P1, P2, P3, r1, r2, r3):
        r'''
        Find whether 3 spheres intersect
        '''
        temp1 = P2-P1
        e_x = temp1/np.linalg.norm(temp1, axis=1)[:, np.newaxis]
        temp2 = P3-P1
        i = self._my_dot(e_x, temp2)[:, np.newaxis]
        temp3 = temp2 - i*e_x
        e_y = temp3/np.linalg.norm(temp3, axis=1)[:, np.newaxis]
        d = np.linalg.norm(P2-P1, axis=1)[:, np.newaxis]
        j = self._my_dot(e_y, temp2)[:, np.newaxis]
        x = (r1*r1 - r2*r2 + d*d) / (2*d)
        y = (r1*r1 - r3*r3 - 2*i*x + (i*i) + (j*j)) / (2*j)
        temp4 = r1*r1 - x*x - y*y
        return temp4 >= 0