Find the vector equation of the plane ` vec r=(1+s-t) hat i+(2-s) hat j+(3-2s+2t) hat k` in non-parametric form.

Explanation

`vec{r}=(1+s-t) hat{i}+(2-s) hat{j}+(3-2 s+2 t) hat{k} `

`Rightarrow vec{r}=(hat{i}+2 hat{j}+3 hat{k})+s(hat{i}-j-2 hat{k})+t(-hat{i}+0 hat{j}+2 hat{k})`



We know that `vec{r}=vec{a}+s vec{b}+t vec{c}` represents a plane passing through a point whose position vector is `vec{a}` and parallel to the vectors`vec{b}` and `vec{c}.`

Here,` vec{a}=hat{i}+2 hat{j}+3 hat{k} ; vec{b}=hat{i}-j-2 hat{k} ; vec{c}=-hat{i}+0 hat{j}+2 hat{k}`

Normal vector, `vec{n}=vec{b} times vec{c}`


...