Find the expression in the vector form for point $\vec{r_1}$ of intersection of plane $\vec{r}.\vec{n}=d$ and the perpendicular line $\vec{r}=\vec{r_0}+t \vec{n}$ where $t$is the parameter.
As $\vec{r_1}$ lies on both line and plane, hence
$\vec{r_1}.\vec{n}=d$
and
$\vec{r_1}=\vec{r_0}+t \vec{n}$ Now in second equation I took dot product with $\vec{n}$ to get
$\vec{r_1} \cdot \vec{n}=\vec{r_0}\cdot \vec{n}+t |\vec{n}|^2$
which gives value of $d$ but how will we separate $\vec{r_1}$ here? Could someone help me with this?