Line and Plane — Maths STD 12 Science — Question

The vector equation of the line passing through the $A(\bar{a})$ and $B(\bar{b})$ is $\bar{r}=\bar{a}+\lambda(\bar{b}-\bar{a}), \lambda$

is a scalar

∴ the vector equation of the line passing through the points having position vectors

$3 \hat{i}+4 \hat{j}-7 \hat{k}$ and $6 \hat{i}-\hat{j}+\hat{k}$ is

is $\bar{r}=(3 \hat{i}+4 \hat{j}-7 \hat{k})+\lambda[(6 \hat{i}-\hat{j}+\hat{k})-(3 \hat{i}+4 \hat{j}-7 \hat{k})]$

i.e. $\bar{r}=(3 \hat{i}+4 \hat{j}-7 \hat{k})+\lambda(3 \hat{i}-5 \hat{j}+8 \hat{k})$.