Find the angle between the plane: ` vec rdot((2 hat i-3 hat j+4 hat k)=1\ a n d\ vec rdot((- hat i+ hat j)=4` .

Explanation

Here it is given that , `vec{r} cdot(2 vec{i}-3 vec{j}+4 vec{k})=1` quad (1)


`vec{r} cdot(-vec{i}+vec{j})=4`

So, the angle b/w (1) and (i1) is equal to angle b/w `D R^{prime}`
D R of plane 1`=2 vec{i}-3 vec{j}+4 vec{k}=n_{1}`

`DR of plare 2=-vec{i}+vec{j}=n_{2}`


`cos theta=|frac{n_{1} cdot n_{2}}{|n_{1}| cdot|n_{2}|}|=frac{(2 vec{i}-3 vec{j}+4 vec{k})(-vec{i}+vec{j})}{sqrt{4+9+16 sqrt{1+1}}}`

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