L₁ = $$\overrightarrow r = \left( {\widehat i - \widehat j} \right) + l\left( {2\widehat i + \widehat k} \right)$$

= $$\widehat i\left( {1 + 2l} \right) + \widehat j\left( { - 1} \right) + \widehat k\left( l \right)$$

L₂ = $$\overrightarrow r = \left( {2\widehat i - \widehat j} \right) + m\left( {\widehat i + \widehat j + \widehat k} \right)$$

= $$\widehat i\left( {2 + m} \right) + \widehat j\left( {m - 1} \right) + \widehat k\left( { - m} \right)$$

Equating coefficient of $$\widehat i$$, $$\widehat j$$ and $$\widehat k$$ of L₁ and L₂

2l + 1 = m + 2 ... (1)

–1 = –1 + m ...(2)

l = –m ...(3)

from (ii) m = 0

from (iii) $$l$$ = 0

These values of m and $$l$$ do not satisfy equation (1).

Hence the two lines do not intersect for any values of $$l$$ and m.