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  • Let  be the angle between the planes and  <img alt="P_1: \vec{r} \cdot(\hat{\imath}+\hat{\jmath}+2

Let \theta be the angle between the planes and  P_1: \vec{r} \cdot(\hat{\imath}+\hat{\jmath}+2 \hat{k})=9 \:  and  P_2: \vec{r} \cdot(2 \hat{\imath}-\hat{\jmath}+\hat{k})=15  Let L be
the line that meets P_2  at the point (4, −2,5) and makes an angle \theta with the normal of  P_2 . If α is the
angle between L and  P_2 , then (tan2 θ)(cot2 α) is equal to

Option: 1

9


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\begin{aligned} & \cos \theta=\frac{\langle 1,1,2\rangle \cdot\langle 2,-1,1\rangle}{6} \\ & =\frac{2-1+2}{6}=\frac{1}{2} \\ & \theta=\frac{\pi}{3} \end{aligned}

then  \frac{\pi}{2}-\alpha=\frac{\pi}{3}  

\begin{gathered} \alpha=\frac{\pi}{6} \\ \left(\tan ^2 \theta\right)\left(\cot ^2 \alpha\right)=(\sqrt{3})^2 \times(\sqrt{3})^2=9 \end{gathered}

 

Posted by

Nehul

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