The lattice constant of a simple cubic lattice is a0.
(a) sketch the following planes:
(i) (110),
(ii) (111),
(iii) (220), and (iv) (321).
(b) sketch the following directions:
(i) [110],
(ii) [111],
(iii) [220], and (iv) [321]

A)The sketches for the required planes were drawn in the first attachment.

B)The sketches for the required directions were drawn in the second attachment.

To draw a plane in a simple cubic lattice, you have to follow these instructions:

1- the cube has 3 main directions called "a", "b" and "c" (as shown in the first attachment)

2- The coordinates of that plane are written as: π:(1/a₀ 1/b₀ 1/c₀) (if one of the coordinates is 0, for example (1 1 0), c₀ is ∞, therefore that plane never cross the direction c).

3- Identify the points a₀, b₀, and c₀ at the plane that crosses this main directions and point them in the cubic cell.

4- Join the points.

To draw a direction in a simple cubic lattice, you have to follow these instructions:

1- Identify the points a₀, b₀, and c₀ in the cubic cell.

2- Draw the direction as a vector-like (a₀ b₀ c₀).

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