CAIE A-Level Mathematics A2 3.7.5 Whether Two Lines Are Parallel Questions

Use components to form two relevant equations in 2 unknowns
For their $l_{1} \mathrm{~B} 0$ if they use the same unknown for both lines.

B1FT

Two components of $\left(\begin{array}{c}5+\lambda 2+\lambda -\lambda\end{array}\right)=\left(\begin{array}{c}-2+3 \mu 1+\mu 4-2 \mu\end{array}\right)$ seen or implied.

Solve 2 relevant equations in 2 unknowns for $\lambda$ or $\mu$
For their $l_{1}$.

Obtain $\lambda=2$ or $\mu=3$
Or equivalent e.g. using $\overrightarrow{B C}$ as direction vector gives $\lambda=\frac{2}{3}$.

Obtain (7,4,-2)

No need to check the third equation - the question implies that the lines intersect.
Accept position vector. Condone a column vector with i, j, k.
SC: B1 M1 A1 A1 if one component of their line is incorrect but they do not use that component.