A line with d.r's (2,7,-5) is drawn to intersect the lines 3. x-5 y-7 z+2 and -3 x+3 y-3 z-6 -1 2 4 at P and Q respectively. Length of PQ is 1) V78 2) J77 3) 54 4) 74 . If the angle between the line x=: y-1z-3 and the plane x +2y +3z = 4is cos(/5/14) then 2= 3 2) 3 3) 11. A tetrahedron has vertices at O(0, 0, 0) A(1, 2, 1), B(2, 1, 3), and C(-1, 1, 2). Then the angle between the faces OAB and ABC will be 19 1) cos 17 2) cos 31 35 (A 3) 30 4) 900 12. The two lines x= ay + b, z = cy + d and x a'y + b', z c'y + d' will be perpendicular, if and only if 1) aa'+ bb'+ cc' + 1 = 0 2) aa'+ bb'+ cc' = 0 3) (a + a)(b + b)(c + c') = 0 4) aa'+ cc' + 1 = 0 13. The value of k if the lines -3 x+1 y+2 z-3 2k (2 x-1y+5 z+6 and 3k may be perpendicular %3D 1y5 7 1) 3 2) 2 3) -2 4) 4 x+1 14. If the angle e between the line 1 1 z-2 and the plane 2.x-y+VAz+4=0 is such that (E sine = the value of a is 5 1) 3 3 3) 2) 4 4) 15. The angle between the lines 2x 3y zand 6x =-y = -4z is -(S 1) 0 2) 90 3) 450 4) 30 Shortest distance,Foot, Image, Length of the perpendicualr and Coplanar : 16. The shortest distance between the lines x y x+2 and -1 -4 z-5 lies in the interval 4. 2 2 1 8. 1) [0, 1) 2) [1, 2) 3) (2, 3] 4) (3, 4] 2/5