Find the shortest distance between the following two lines: ` vec r=(1+lambda) hat i+(2-lambda) hat j+(lambda+1) hat k` ; ` vec r=(2 hat i- hat j- hat k)+\ mu\ (2 hat i+ hat j+2 hat k)`

Find the shortest distance between the lines vec r=(1-lambda)hat i+(lambda-2)hat j+(3-2 lambda)hat k and vec r=(mu+1)hat i+(2 mu+1)hat k

By computing the shortest distance determine whether the following pairs of lines intersect or not: vec r=( hat i- hat j)+lambda(2 hat i+ hat k)a n d vec r=(2 hat i- hat j)+mu( hat i+ hat j- hat k) vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat j)a n d vec r=(4 hat i- hat k)+mu(2 hat i+3 hat k) . (x-1)/2=(y+1)/3=za n d(x+1)/5=(y-2)/1; z=2 (x-5)/4=(y-7)/(-5)=(z+3)/(-5)a n d(x-8)/7=(y-7)/1=(z-5)/3 .

By computing the shortest distance determine whether the following pairs of lines intersect or not : -> r=( hat i- hat j)+lambda(2 hat i+ hat k)a n d\ -> r=(2 hat i- hat j)+mu( hat i+ hat j- hat k)dot

Find the shortest distance between the following lines whose vector equations are: vec r=(1-t)hat i+(t-2)hat j+(3-2t)hat k and vec r=(s+1)hat i+(2s-1)hat j-(2s+1)hat k

Find the 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)) + mu (2hat(i) + 4hat(j) - 5hat(k))

Find the shortest distance between the straight lines vec r=(3hat i+hat j+2hat k)+lambda(hat i+2hat j-hat k) and vec r=(2hat i-3hat j+hat k)+mu(2hat i-hat j+3hat 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 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 whose vector equations are quad vec r=(1-t)hat i+(t-2)hat j+(3-2t)hat k and vec r=(s+1)hat i+(2s-1)hat j-(2s+1)hat k

Find the 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)+mu(2hat i+4hat j-5hat k)