a. Line x−1−2=y+23=z−1  is along with  vector a→=−2i^+3j^−k^ and line       r→=(3i^−j^+k^)+t(i^+j^+k^)  is along the vector b→=i^+j^+k^. Here a→⊥b→       Also 3−1−1−(−2)1−0−23−1111≠0b.  The direction ratios of the line x - y + 2z - 4 = 0      =2x+y−3z+5=0 are i^j^k^1−1221−3=i^+7j^+3k^.        Hence  the given two lines are parallelc.  The given ,ty are    (x=t−3,y=−2t+1,z=−3t−2) and r→=(t+1)i^+(2t+3)j^+(−t−9)k^     x+31=y−1−2=z+2−3 and x−11=y−32=z+9−1       The lines are perpendicular as  1(1) + (-2) (2) + (-3) (-1) = 0.       Also −3−11−3−2−(−9)1−2−312−1=0      Hence, the lines are intersectingd.  The given lines are  r→=(i^+3j^−k^)+t(2i^−j^−k^) and r→=(−i^−2j^+5k^)+si^−2j^+34k^       1−(−1)3−(−2)−1−52−1−11−23/4=0       Hence, the lines are coplanar and intersecting (as the lines are not parallel).