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2 problems match “angle between line and plane”. Clear

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1. Coefficient from line-plane angle ●●●○○ 50 ptsThe angle between the plane $3x + by - 5z = 2$ and the straight line $x + 2 = \frac{3 - y}{2} = \frac{z - 1}{2}$ is $45^\circ$. Find the constant $b$, given that $0 < b < 10$.
2. Sum of squared tangents in a tetrahedron section ●●●●○ 100 ptsA regular tetrahedron is intersected by a plane that is perpendicular to one of its faces and meets that face along a line $e$. The intersection lines of this plane with the other three face planes of the tetrahedron form angles $\varphi_1, \varphi_2, \varphi_3$ with $e$. Determine the value of $\tan^2 \varphi_1+\tan^2 \varphi_2+\tan^2 \varphi_3$.