The lattice is one of the seven primitive three-dimensional lattices in which the relationship between the lattice vectors a, b, and c can be written as: a = b ≠ c

Tetragonal and hexagonal.

Step-by-step explanation:

In the seven crystal system, one divides the bravais Lattices into the 7 crystals system which are defined by the length a, b, c and the angles alpha, beta, and gamma.

Length of cubic Crystal lattice is same therefore length a=b=c for cubic

. for the Tetragonal and hexagonal.

Although in  Tetragonal α=β=γ=90° and in Hexagonal α=120°, β=γ=90°.

Monoclinic have different length like .

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!