Consider the `L_1:(x+1)/3=(y+2)/1=(z+1)/2 and L_2:(x-2)/1=(y+2)/2=(z-3)/3` The shortest distance betwen `L_1 and L_2` is
(A) 0 (B) `17/sqrt(3)` (C) `41/(5(3)` (D) `17/sqrt(75)`

A paragraph has been given. Based upon this paragraph, 3 multiple choice question have to be answered. Each question has 4 choices a,b,c and d out of which ONLYONE is correct. Consider the L_1:(x+1)/3=(y+2)/1=(z+1)/2 and L_2:(x-2)/1=(y+2)/2=(z-3)/3 The unit vector perpendicular to both L_1 and L_2 is (A) (-hati+7hatk+7hatk)/sqrt(99) (B) (-hati-7hatk+5hatk)/(5sqrt(3)) (C) (-hati+7hatk+7hatk)/(5sqrt(3)) (D) (7hati-7hatk-7k)/sqrt(99)

Read the following passage and answer the questions. Consider the lines L_(1) : (x+1)/(3)=(y+2)/(1)=(z+1)/(2) L_(2) : (x-2)/(1)=(y+2)/(2)=(z-3)/(3) Q. The shortest distance between L_(1) and L_(2) is

Consider the line L 1 : x +1/3 = y+ 2/1= z +1/2 L2 : x-2/1= y+2/2= z-3/3 The unit vector perpendicular to both L 1 and L 2 lines is

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

Consider the line L_(1) : (x-1)/(2)=(y)/(-1)=(z+3)/(1), L_(2) : (x-4)/(1)=(y+3)/(1)=(z+3)/(2) find the angle between them.

Consider the line L 1 : x 1 y 2 z 1 312 +++ ==, L2 : x2y2z3 123

Consider the line L 1 : x 1 y 2 z 1 312 +++ ==, L2 : x2y2z3 123

L_(1):(x+1)/(-3)=(y-3)/(2)=(z+2)/(1),L_(2):(x)/(1)=(y-7)/(-3)=(z+7)/(2) The lines L_(1) and L_(2) are -

Read the following passage and answer the questions. Consider the lines L_(1) : (x+1)/(3)=(y+2)/(1)=(z+1)/(2) L_(2) : (x-2)/(1)=(y+2)/(2)=(z-3)/(3) Q. The distance of the point (1, 1, 1) from the plane passing through the point (-1, -2, -1) and whose normal is perpendicular to both the lines L_(1) and L_(2) , is

If L_1 is the line of intersection of planes 2x+y+z=1a n d3x+y+2z=2a n dL_2 is line x=y=z , Which option is correct? (a)Shortest distance between L_1a n dL_2i s1/(sqrt(2)) Equation of L_1i s(x-1)/1=(y+1)/(-1)=(z-0)/(-1) (b)Shortest distance between L_1a n dL_2 is sqrt(2) Equation of L_1i s(x-1)/1=(y+1)/(-2)=(z-0)/(-1) (c) None of these