Find the shortest distance between the lines l1 and l2 whose vector equations are ` -> r= hat i+ hat j+lambda(2 hat i- hat j+ hat k)` (1)and ` -> r=2 hat i+ hat j-k+mu(3 hat i-5 hat j+2 hat k)` (2)

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)

Find the shortest distance between the following pairs of parallel lines whose equation are: -> r=( hat i+ hat j)+lambda(2 hat i- hat j+ hat k)a n d\ -> r=(2 hat i+ hat j- hat k)+mu(4 hat i-2 hat j+2 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 following pairs of parallel lines whose equation are: -> r=( hat i+2 hat j+3 hat k)+lambda( hat i- hat j+ hat k)a n d\ -> r=(2 hat i- hat j- hat k)+mu(- hat i+ hat j- hat 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

Let the line of the shortest distance between the lines L_1 : vec r = (hat i 2 hat j 3 hat k) lambda (hat i - hat j hat k) and L_2 : vec r = (4 hat i 5 hat j 6 hat k) mu (hat i hat j - hat k) intersect L_1 and L_2 at P and Q respectively. If (alpha, beta, gamma) is the mid point of the line segment PQ, then 2(alpha beta gamma) is equal to ___________.

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 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

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 lines: -> r=6 hat i+2 hat j+2 hat k+lambda( hat i-2 hat j+2 hat k)a n d\ -> r=-4 hat i- hat k+mu(3 hat i-2 hat j-2 hat k)dot