Let \theta be the angle between the planes P_1=\overrightarrow{r} \cdot(\stackrel{ ⋀}{i}+\stackrel{ ⋀}{i}+2\stackrel{ ⋀}{k})=9 and P_2=\overrightarrow{r} \cdot(2 \stackrel{ ⋀}{i}-\stackrel{ ⋀}{i}+\stackrel{ ⋀}{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 \alpha is the angle between L and P_2 then (\tan ^2 \theta) (\cot ^2 \alpha) is equal to _______. [31-Jan-2023 Shift 1]

Three Dimensional Geometry Part 3

Section: Mathematics

Question : 65 of 100

Marks: +1, -0

Let θ be the angle between the planes P1=

→

⋅(

⋀

)=9 and P2=

→

⋅(2

⋀

−

⋀

)=15.
Let L be the line that meets P2 at the point (4,−2,5) and makes an angle θ with the normal of P2. If α is the angle between L and P2 then (tan2θ)(cot2α) is equal to _______.

[31-Jan-2023 Shift 1]

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