We are given with two lines.

…(i)

…(ii)

Take equation (i),

…(iii)

We know that,

Vector equation of a line passing through a point and parallel to a vector is , where λ ∈ ℝ.

Comparing it with equation (iii), we get

Now, take equation (ii),

…(iv)

Similarly from (iv),

So,

Shortest distance between two lines is given by

Solve .

Take 1^st row and 1^st column, multiply the first element of the row (a₁₁) with the difference of multiplication of opposite elements (a₂₂ × a₃₃ – a₂₃ × a₃₂), excluding 1^st row and 1^st column.

Here,

Now take 1^st row and 2^nd column, multiply the second element of the row (a₁₂) with the difference of multiplication of opposite elements (a₂₁ × a₃₃ – a₂₃ × a₃₁), excluding 1^st row and 2^nd column.

Here,

Similarly, take 1^st row and 3^rd column, multiply the third element of the row (a₁₃) with the difference of multiplication of opposite elements (a₂₂ × a₃₃ – a₂₃ × a₃₂), excluding 1^st row and 3^rd column.

Here,

Further, simplifying it.

…(v)

And,

…(vi)

Now, solving .

…(vii)

Substituting values from (v), (vi) and (vii) in d, we get

⇒ d = 14

Thus, the shortest distance between the given lines is 14 units.