The shortest distance between the straight lines through the points `A_1 = (6,2,2)` and `A_2=(-4,0,-1),` in the directions of `(1, -2,2)` and `(3,-2,-2)` is

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

The shortest distance between the line passing through the point (2,-1,1) and parallel to the vector (-1,1,2) and the line passing through (0,3,1) and parallel to vector (2,4,-1) is

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

The shortest distance between the line " 2x-3y+1=0 " and the parabola " y^(2)=4x " ,is

The shortest distance between the straight lines (x-6)/(1)=(2-y)/(2)=(z-2)/(2)" and "(x+4)/(3)=(y)/(-2)=(1-z)/(2) is

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)

Show that the line through the points : (a) (1, -1, 2), (3,4,-2) is perpendicular to the line through the points (0,3,2) and (3, 5,6) (b) (4,7,8) , (2,3,4) is parallel to the line through the points (-1, -2, 1 ) and (1,2,5) .

Write the formula for the shortest distance between the lines -> r= -> a_1+lambda -> b\ a n d\ -> r= -> a_2+mu -> bdot\

Let L be the line created by rotating the tangent line to the parabola y=x^2 at the point (1,1), about A by an angle (-pi/4). Let B be the other intersection of line L with y=x^2. If the area inclosed by the L and the parabola is (a_1/a_2) where a_1 and a_2 are co prime numbers, find(a_1+a_2)