Find the distance between the line ` vec r=(- hat i+3 hat k)+lambda( hat i-2 hat j)` and the line passing through `(0,-1,2)a n d(1,-2,3)dot`

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 lines vec r*(hat i+2hat j-hat k)+lambda(hat i-hat j+hat k) and the plane vec r*(2hat i-hat j+hat k)=4

Find the angle between the line vec r=hat i+2hat j-hat k+lambda(hat i-hat j+hat k) and the plane vec r*(2hat i-hat j+hat k)=4

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 line -> r=(2 hat i+3 hat j+9 hat k)+lambda(2 hat i+3 hat j+4 hat k) and the plane -> r(dot( hat i+ hat j+ hat k))=5.

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=(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)

The image of the point (1,2,3) about the line vec r=(2hat i+3hat j-hat k)+lambda(hat i2hat j+2hat k) is

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