Question

Find the points of intersection of the following pair of lines:

$\overline{r}=\overline{b}-2\overline{c}+\lambda (\overline{a}+\overline{b}),\overline{r}=2\overline{b}-\overline{c}+\mu (\overline{b}+\overline{c})$

• A. The lines intersect at the point $b-2c$
• B. The lines intersect at the point $a+b-2c$
• C. The lines intersect at the point $3b$
• D. The lines intersect at the point $2a+3b-2c$

Answer 1

The correct option is A The lines intersect at the point $b-2c$

Given lines

$r=b-2c+\lambda (a+b)$--------(1)

$r=2b-c+\mu (b+c)$--------(2)

To find point of intersection

$\Rightarrow$$b-2c+\lambda (a+b)=2b-c+\mu (b+c)$

$\Rightarrow$ $-2c+\lambda a=(2+\mu )b+(\mu -1)c$

comparing both sides, we get,

$\Rightarrow$$\mu -1=-2$

$\Rightarrow$$\mu =-1$

$\Rightarrow$$1+\lambda =2-1$

$\Rightarrow$$\lambda =0$

putting $\lambda =0$ in eq $\left(1\right)$

$\Rightarrow$$r=b-2c$

therefore the point of intersection$\Rightarrow$ $b-2c$