Find the distance between the parallel planes ` vec rdot( hat i+2 hat j+3 hat k)+7=0a n d vec rdot(2 hat i+4 hat j+6 hat k)+7=0.`

Explanation

The given equation of planes are :


`vec{r} cdot(hat{i}+2 hat{j}+3 hat{k})+7=0 `

and `vec{r} cdot(2 hat{i}+4 hat{j}+6 hat{k})+7=0 `

`Rightarrow(hat{i}+y hat{j}+zk)(hat{i}+2 hat{j}+3 hat{k})+7=0`

`Rightarrow x+2 y+3 z+7=0 quad ldots ldots . .(1) `

`Rightarrow(hat{i}+y hat{j}+z hat{k})(2 hat{i}+4 hat{hat{j}}+6 hat{k})+7=0 `

`Rightarrow 2 x+4 y+6 z+7=0 quad ldots ldots ldots .(2)`

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