Let the two lines be l₁ and l₂.

So, and

We need to find the shortest distance between l₁ and l₂.

Recall the shortest distance between the lines: and is given by

Here, (x₁, y₁, z₁) = (2, 5, 0) and (x₂, y₂, z₂) = (0, –1, 1)

Also (a₁, b₁, c₁) = (–1, 2, 3) and (a₂, b₂, c₂) = (2, –1, 2)

We will evaluate the numerator first.

Let

⇒ N = (–2)[(2)(2) – (–1)(3)] – (–6)[(–1)(2) – (2)(3)] + (1)[(–1)(–1) – (2)(2)]

⇒ N = –2(4 + 3) + 6(–2 – 6) + (1 – 4)

⇒ N = –14 – 48 – 3

∴ N = –65

Now, we will evaluate the denominator.

Let

b₁c₂ – b₂c₁ = (2)(2) – (–1)(3) = 4 – (–3) = 7

c₁a₂ – c₂a₁ = (3)(2) – (2)(–1) = 6 – (–2) = 8

a₁b₂ – a₂b₁ = (–1)(–1) – (2)(2) = 1 – 4 = –3

So, shortest distance =

Thus, the required shortest distance is units.