Explain the origin of the rock cleavage seen in slate and the
mineral cleavage seen in amphibole or calcite.

Cleavage of a mineral is defined as the direction along which the mineral breaks over the flat mineral surface. It is directly dependent on the mineral's crystallographic structure.

Slaty cleavage refers to the cleavage that is commonly found in the low grade metamorphic rock slate. Here, the fine grained minerals are so closely spaced and the lines of weakness are all parallel to each other, that allows the minerals to break in fine and thin layers. During the time of formation of slate, the smaller fractures are formed due to the increasing pressure. When groundwater moves through these fractures it forms a weak zone due to which these slaty cleavage forms.

When the rocks undergoes deformation and changes in the pressure and temperature condition then the cleavages are formed on the mineral's surface. The calcite contains rhombohedral cleavage are considered to be the perfect cleavage. Whereas the cleavage in amphibole is uneven and comprised of two directions that intersect each other at 56° and 124°.