Determine the value of `lambda` for which the following plane are perpendicular to each other. ` vec rdot(( hat i+2 hat j+3 hat k)=7\ a n d\ vec rdot((lambda hat i+2 hat j-7 hat k)=26.`

Explanation

Given:

` vec{r} cdot(1+2 hat{j}+3 hat{k})=7 `and `vec{r} cdot(lambda hat{i}+2 {j}-7 hat{k})=26`

`vec{n}_{1}=hat{1}+2 hat{j}+3 hat{k} and vec{n}_{2}=lambda hat{1}+2 hat{jmath}-7 hat{k}`

It is known that two planes are said to be perpendicular to each other if

`n_{1} cdot n_{2}=0`

Consider

`{n}_{1}, {n}_{2}=(hat{{l}}+2 hat{{j}}+3 hat{{k}})(lambda hat{{l}}+2 hat{{j}}-7 hat{k})`

`Rightarrow lambda+4-21=0`

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