Question

$\mathrm{If}\mathrm{two}\mathrm{lines}{L}_1=a_1+{\mathrm{\lambda b}}_1\mathrm{and}{L}_2=a_2+{\mathrm{\lambda b}}_2\mathrm{are}\mathrm{such}\mathrm{that}{b}_1\mathrm{is}\mathrm{parallel}\mathrm{to}{b}_2\mathrm{and}{a}_1\ne a_2,\mathrm{then}{L}_1\mathrm{and}{L}_2\mathrm{will}\mathrm{be}$

• A. coincident lines
• B. intersecting lines
• C. parallel lines
• D. perpendicular lines

Answer 1

The correct option is C parallel lines

We know that the direction for a given line depends on the direction vector component of line that is $b_i$ in $L_i=a_i+{\mathrm{\lambda b}}_i$ Here it is given that $b_1$ is parallel to $b_2$ So, $L_1$ and $L_2$ can be parallel or coincident, but since $a_1\ne a_2$, the lines do not passes through same point and hence they will be parallel to each other but not coincident.