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 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 whose vector equations are vec r=(hat i+2hat j+3hat k)+lambda(hat i-3hat j+2hat k) and vec r=4hat i+5hat j+6hat k+mu(2hat i+3hat j+hat k)

Find the shortest distance between the lines 11 and 12 whose vector equations are quad vec r=hat i+hat j+lambda(2hat i-hat j+hat k) (1) and quad vec r=2hat i+hat j-k+mu(3hat i-5hat j+2hat 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 .

Find the vector equation of the plane vec r=(1+s-t)hat i+(2-s)hat j+(3-2s+2t)hat k in non-parametric form.

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

Find the Cartesian form the equation of the plane vec r=(s-2t)hat i+(3-t)hat j+(2s+t)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

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)