Find the Cartesian as well as vector equations of the planes through the intersection of the planes ` vec rdot((2 hat i+6 hat j)+12=0\ a n d\ vec rdot((3 hat i- hat j-4 hat k)=0` which are at a unit distance from the origin.

Explanation

`vec{r}.(2 hat{i}+6 hat{j})+12=0 Rightarrow 2 x+6 y+12=0 `

`vec{r}.(3 hat{i}-hat{j}+4 hat{k})=0 Rightarrow 3 x-y+4 z=0`


Intersecting plane equation is


`2 x+6 y+12+lambda(3 x-y+4 z)=0`



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