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  1. Angle between two lines in space ●○○○○ 10 ptsFind the angle between the lines L1:x=−1+3t, y=1+4t, z=−2tL_1: x=-1+3t,\ y=1+4t,\ z=-2t and L2:x=−1+2s, y=3s, z=−7+sL_2: x=-1+2s,\ y=3s,\ z=-7+s, taken as the angle between their direction vectors ⟨3,4,−2⟩\langle 3,4,-2\rangle and ⟨2,3,1⟩\langle 2,3,1\rangle. Give the angle in degrees. Round to one decimal place.
  2. Angle between two lines ●●○○○ 20 ptsFind the angle between the lines l1:3x−y+2=0l_1: \sqrt{3}x - y + 2 = 0 and l2:3x+3y−5=0l_2: 3x + \sqrt{3}y - 5 = 0, in degrees.
  3. Angle between lines from direction cosines ●●●○○ 50 ptsTwo lines have direction cosines (l1,m1,n1)(l_1,m_1,n_1) and (l2,m2,n2)(l_2,m_2,n_2). Each line satisfies l+m+n=0l+m+n=0 and mnq−r+nlr−p+lmp−q=0\frac{mn}{q-r}+\frac{nl}{r-p}+\frac{lm}{p-q}=0, where pp, qq, rr are distinct constants. Find the acute angle between the two lines, in degrees.