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3 problems match “vectors in space”. 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. Angle between two vectors ●○○○○ 10 ptsGiven vectors $\overrightarrow{a} = (0, 2, 1)$ and $\overrightarrow{b} = (-1, 1, -2)$, find the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ in degrees.
3. Area of a space quadrilateral ●●○○○ 20 ptsThe points $A = (3,-4,2)$, $B = (5,-8,5)$, $C = (4,-3,0)$, and $D = (6,-7,3)$ in space form a flat quadrilateral. Find the area of this quadrilateral. Round to two decimal places.