The shortest distance between the straighat lines through the point `A_1=(6,2,2) and A_2=(-4,0,-1)` in the directions `1,-2,2 and 3,-2,-2` is
(A) 6 (B) 8 (C) 12 (D) 9

Show that the line through the points (1, 1, 2), (3, 4, 2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).

Write the formula for the shortest distance between the lines vec r= vec a_1+lambda vec b_1 a n d\ vec r= vec a_2+mu vec b_2dot\

Direction cosines of a line which passes through the points (1,2,3) and (-3,4,1) is A) (4/(2sqrt6), -2/(2sqrt6), 2/(2sqrt6)) B) (4/(2sqrt6), -2/(2sqrt6), -2/(2sqrt6)) C) (4/(2sqrt6), 4/(2sqrt6), 2/(2sqrt6)) D) (-4/(2sqrt6), 1/(2sqrt6), -2/(2sqrt6))

The shortest distance between line y-x=1 and curve x=y^2 is (a) (3sqrt2)/8 (b) 8/(3sqrt2) (c) 4/sqrt3 (d) sqrt3/4

The shortest distance form the point (1,2,-1) to the surface of the sphere (x+1)^(2)+(y+2)^(2)+(z-1)^(2)=6 (A) 3sqrt(6) (B) 2sqrt(6) (C) sqrt(6) (D) 2

If each a_i > 0 , then the shortest distance between the points (0,-3) and the curve y=1+a_1x^2+a_2 x^4+.......+a_n x^(2n) is

The line passing through the points (5, 1, a) and (3, b, 1) crosses the yzplane at the point (0,(17)/2,(-13)/2) .Then (1) a""=""2,""b""=""8 (2) a""=""4,""b""=""6 (3) a""=""6,""b""=""4 (4) a""=""8,""b""=""2

The ratio in which the line segment joining points A(a_1,\ b_1) and B(a_2,\ b_2) is divided by y-axis is (a) -a_1: a_2 (b) a_1: a_2 (c) b_1: b_2 (d) -b_1: b_2

If A_1 and A_2 are two AMs between a and b then (2A_1 -A_2) (2A_2 - A_1) =

The capacitance of the capacitors of plate areas A_1 and A_2(A_1 lt A_2) at a distance d is