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3 problems match “direction vectors”. Clear

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1. Angle between two lines in space ●○○○○ 10 ptsFind the angle between the lines $L_1: x=-1+3t,\ y=1+4t,\ z=-2t$ and $L_2: x=-1+2s,\ y=3s,\ z=-7+s$, taken as the angle between their direction vectors $\langle 3,4,-2\rangle$ and $\langle 2,3,1\rangle$. Give the angle in degrees. Round to one decimal place.
2. Inclination angle from a direction vector ●○○○○ 10 ptsThe direction vector of the line $l$ has coordinates $(2, 2\sqrt{3})$. Find the inclination angle of the line $l$ in degrees, where the angle lies in $[0^\circ, 180^\circ)$.
3. 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 $0 < b < 10$.