Vector Equation for Straight Line

Q.

Vector equation of a straight line passing through a point given by position vector $\overline{a}$ parallel to $\overline{b}$ be is given by $\overline{r}=\overline{a}-\lambda \overline{b},where\overline{r}$ , where $\overline{r}$ is r position vector of a general point on the line and $\lambda ϵIR$

1. True

2. False

Q. In a triangle $ABC,$ a point $P$ is chosen on side $\overrightarrow{AB}$ such that $AP:PB=1:4$ and a point $Q$ is chosen on side $\overrightarrow{BC}$ such that $CQ:QB=1:3.$ Line segment $\overrightarrow{CP}$ and $\overrightarrow{AQ}$ intersect at $M.$ If the ratio $\frac{MC}{PC}$ is expressed as a rational number in the lowest term as $\frac{a}{b},$ then $b-a$ equals

Q. $\mathrm{In}\mathrm{the}\mathrm{given}\mathrm{two}\mathrm{lines}{L}_1=a_1+{\mathrm{\lambda b}}_1\mathrm{and}{L}_2=a_2+{\mathrm{\lambda b}}_2,\mathrm{if}{b}_1=b_2\mathrm{then}\mathrm{the}\mathrm{lines}\mathrm{will}\mathrm{be}\mathrm{definitely}\mathrm{parallel}.$

1. False
2. True

Q. The median AD of the $\Delta ABC$ is bisected at E, BE meets AC in F, then AF: AC is equal to

1. $\frac{3}{4}$
2. $\frac{1}{3}$
3. $\frac{1}{2}$
4. $\frac{1}{4}$