Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

We have line $\bar{r}=(2\hat{i}+\hat{j}-4\hat{k})+\lambda (\hat{i}-2\hat{j}+2\hat{k})$ Hence coordinates of any point on this line are $(\lambda +2,-2\lambda +1,2\lambda -4)$ This point lies on XOY plane whose equation is $z=0$ $\therefore 2\lambda -4=0\Rightarrow \lambda =2$ Hence point of intersection is $(4,-3,0)$. Thus $\mathrm{pv}$ is $4\hat{\mathrm{i}}-3\hat{\mathrm{j}}$