Assume the dipole model of earth's magnetic field B which is given by `B_V`= vertical component of magnetic field `=(mu_0)/(4pi)(2Mcos theta)/(r^3)`, `B_H`=Horizontal component of magnetic field `=(mu_0)/(4pi)(sin theta M)/(r^3)`, `theta=90^@`-latitude as measured from magnetic equator.
Find loci of points for which (i) `|vecB|` is minimum, (ii) dip angle is zero, and (iii) dip angle is `+-45^@`.

Explanation

To solve the problem, we need to analyze the given equations for the vertical and horizontal components of the Earth's magnetic field and derive the required conditions step by step.

### Given:
1. Vertical component of magnetic field:
\[ B_V = \frac{\mu_0}{4\pi} \frac{2M \cos \theta}{r^3} \]
2. Horizontal component of magnetic field:
...