Show that the following planes are at right angle: ` vec rdot((2 hat i- hat j+ hat k)=5\ a n d\ vec rdot((- hat i- hat j+ hat k)=3.`

Explanation

Given:

`vec{r} cdot(2 hat{1}-hat{j}+hat{k})=5` and `vec{r} cdot(-hat{1}-hat{j}+hat{k})=3`


`vec{n_{1}}=2 hat{1}-hat{j}+hat{k}` and `vec{n_{2}}=-hat{1}-hat{j}+hat{k}`


Considering `n_{1} cdot n_{2}=(2 hat{1}-hat{j}+hat{k})(-hat{1}-hat{j}+hat{k})`


`=-2+1+1=0`

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