4. Vectors are not just important in physics-all of the natural world transpires in three dimensions-but they are important for chemistry too. In a methane molecule, CH4, the hydrogen atoms are arranged at the vertices of a regular tetrahedron (each side is an equilat- eral triangle) with the carbon atom at its centre. Place the carbon atom at the origin of your coordinates, and one of the hydrogen atoms at the point 1 = a z along the z-axis, where a is the length of the CH bond. Next, place the three other hydrogen atoms at the vertices of an equilateral triangle below the xy plane: at 12 = acoso x - asinez, 73 = -Jacosex+ Wacosey -asinez, and 7 = -Sacosex - V3 2 acosey - asinez. a. What value should you choose for A so that the distance between any two hydrogen atoms is the same? Hint: try to derive a condition on o from setting some of the distances equal, e.g. 171 - 72ll = 1/73 -721/. b. What is the distance and the angle between neighbouring hydrogen atoms