(i) Express the general point of l or m in component form: l: (3 - λ, -2 + 2λ, 1 + λ) and m: (4 + aμ, 4 + bμ, 2 - μ).

\(Equate components and eliminate either λ or μ from a pair of equations. For example, equate the i components: 3 - λ = 4 + aμ.\)

Eliminate the other parameter and obtain an equation in a and b. For example, equate the k components: 1 + λ = 2 - μ.

\(From these, solve to obtain 2a - b = 4.\)

\((ii) Using the correct process, equate the scalar product of the direction vectors to zero: (-1, 2, 1) ⋅ (a, b, -1) = 0.\)

\(This gives -a + 2b - 1 = 0.\)

\(Solve the simultaneous equations for a and b: 2a - b = 4 and -a + 2b - 1 = 0.\)

\(Obtain a = 3, b = 2.\)

(iii) Substitute found values in component equations and solve for λ or μ.

\(Obtain the position vector i + 2j + 3k from either λ = 2 or μ = -1.\)