Vector Equation for Straight Line

Q. 36. 2x+3y+4=0 and ax+ky+2=0 are identical lines then 3a-2k=

Q. $\mathrm{Which}\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{is}\mathrm{the}\mathrm{vector}\mathrm{equation}\mathrm{of}a\mathrm{line}\mathrm{which}\mathrm{passes}\mathrm{through}\mathrm{point}P(2,-1,4)\mathrm{and}\mathrm{having}\mathrm{the}\mathrm{direction}\mathrm{along}\mathrm{the}\mathrm{vector}\hat{i}+3\hat{j}-2\hat{k}.$

1. 
   $(2+\lambda )\hat{i}+(-1+3\lambda )\hat{j}+(4-2\lambda )\hat{k}$
2. $(2-\lambda )\hat{i}+(-1-3\lambda )\hat{j}+(4+2\lambda )\hat{k}$
3. $(1+2\lambda )\hat{i}+(3-\lambda )\hat{j}+(-2+4\lambda )\hat{k}$
4. $\lambda \hat{i}+3\lambda \hat{j}-2\lambda \hat{k}$

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

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

Q.

Find Equation of a straight line which passes through the points given by position vectors $\overline{a}and\overline{b}$ .

1. $\overline{a}+\lambda \overline{b}$

2. $\overline{a}+\lambda (\overline{a}+\overline{b})$

3. $\overline{b}+\lambda (\overline{a}-\overline{b})$

4. $\overline{a}-\lambda (\overline{a}-\overline{b})$