Find the angel between the following pair of lines: ` vec r=2 hat i-5 hat j+ hat k+lambda(3 hat i+2 hat j+6 hat k)a n d vec r=7 hat i-6 hat k+mu( hat i+2 hat j+2 hat k)` `x/2=y/2=z/1a n d(x-5)/4=(y-2)/1=(z-3)/8`

Find the angle between the following pairs of lines: -> r=(3 hat i+2 hat j-4 hat k)+lambda( hat i+2 hat j+2 hat k)a n d\ -> r=(5 hat i-2 hat k)+mu(3 hat i+2 hat j+6 hat k)dot

vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k) and vec r=(hat i-hat j+2hat k)+mu(2hat i+4hat j-5hat k)

Find the angle between the following pairs of lines: (i) quad vec r=2hat i-5hat j+hat k+lambda(3hat i+2hat j+6hat k) and vec r=3hat i+hat j-2hat k+lambda(hat i-hat j-2hat k)vec r=3hat i+hat j-26hat k+mu(3hat i-5hat j-2hat k)

Find the distance between the lines l_1a n d\ l_2 given by -> r= hat i+2 hat j-4 hat k+lambda(2 hat i+3 hat j+6 hat k)a n d\ ,\ -> r=3 hat i+3 hat j-5 hat k+mu(2 hat i+3 hat j+6 hat k)dot

Find the shortest distance between the lines vec r=(hat i+2hat j+hat k)+lambda(hat i-hat j+hat k) and ,vec r,=2hat i-hat j-hat k+mu(2hat i+hat j+2hat k)

Find the shortest distance between the lines vec r=(hat i+2hat j+hat k)+lambda(hat i-hat j+hat k) and vec r=(2hat i-hat j-hat k)+mu(2hat i+hat j+2hat k)

Find the angle between the following pairs of lines: -> r=lambda( hat i+ hat j+2 hat k)\ a n d\ -> r=2 hat j+mu[(sqrt(3)-1) hat i-(sqrt(3)+1) hat j+4 hat k]dot

Shortest distance between the lines: vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k) and vec r=(hat i-hat j+2hat k)+u(2hat i+4hat j-5hat k)

Find the angle between the line vec r=(2hat i-hat j+3hat k)+lambda(3hat i-hat j+2hat k) and the plane vec r*(hat i+hat j+hat k)=3

Find the angle between the following pairs of lines : (i) vec(r) = 3 hat(i) + 2 hat(j) - 4 hat(k) + lambda (hat(i) + 2 hat(j) + 2 hat(k) ) . vec(r) = 5 hat(j) - 2 hat(k) + mu ( 3 hat(i) + 2 hat(j) + 6 hat(k)) (ii) vec(r) = 3 hat(i) + hat(j) - 2 hat(k) + lambda (hat(i) - hat(j) - 2 hat(k) ) . vec(r) =(2 hat(i) - hat(j) - 56 hat(k)) + mu ( 3 hat(i) - 5 hat(j) - 4 hat(k)) (iii) (x-2)/(2) = (y - 1)/(5) = (z + 3)/(-3) and (x + 2)/(-1) = (y - 4)/(8) = (z - 5)/(4) (iv) (x - 4)/(3) = (y + 1)/(4) = (z - 6)/(5) and (x-5)/(1) = (2y +5)/(-2) = (z - 3)/(1) (v) (5 -x)/(3) = (y + 3)/(-4) , z = 7 and x = (1-y)/(2) = (z - 6)/(2) (vi) (x + 3)/(3) = (y - 1)/(5) = (z + 3)/(4) and (x + 1)/(1) = (y - 4)/(1) = (z-5)/(2) .