Question

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

• A. $\overline{a}+\lambda \overline{b}$
• B. $\overline{a}+\lambda (\overline{a}+\overline{b})$
• C. $\overline{b}+\lambda (\overline{a}-\overline{b})$
• D. $\overline{a}-\lambda (\overline{a}-\overline{b})$

Answer 1

Answer: (B), (C)

The correct options are
B

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

C

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

Let’s see the figure of the line,

If you look closely, the line which passes through points given by position vectors $\overline{a}and\overline{b}$ is parallel to $\overline{a}-\overline{b}$ which makes it a problem of finding the equation of a line given a point and parallel to a line. Therefore, equation of the line will be $\overline{a}+\lambda (\overline{a}-\overline{b})or\overline{b}+\lambda (\overline{a}-\overline{b}),\lambda ϵIR$ . Again without loss of generality. $\overline{a}+\lambda (\overline{a}-\overline{b})$ can be modified to $\overline{a}-\lambda (\overline{a}-\overline{b})and\overline{b}+\lambda (\overline{a}-\overline{b})$. Therefore answers are both options c and d.