Find the vector equation of the line passing through `(2,1,-1)` and parallel to the line `vec r= (hat i+hat j)+lambda(2hat i-hat j+hat k)`. Also, find the distance between these two lines.

Find the equation of a line passing through a point (2, -1, 3) and parallel to the line vec r=( hat i+ hat j)+lambda(2 hat i+ hat j-2 hat k)dot

Find the equation of a line passing through a point (2, -1, 3) and parallel to the line -> r=( hat i+ hat j)+lambda(2 hat i+ hat j-2 hat k)dot

Find the vector equation of the line passing through (1,2,3) and parallel to the planes vec r*(hat i-hat j+2hat k)=5 and vec r*(3hat i+hat j+hat k)=6

Find the vector equation of the line passing through (1,2,3) and parallel to the planes vec r.( hat i- hat j+2 hat k)=5a n d vec r.(3 hat i+ hat j+ hat k)=6.

Find the vector equation of the line passing through the point (1,2) and parallel to the planes vec r*(hat i-hat j+2hat k)=5 and vec r*(3hat i+hat j+hat k)=6

Find the vector equation of a line passing through the point (2,3,2) and parallel to the line : vec(r) = (-2 hat(i) + 3 hat(j) ) + lambda (2 hat(i) - 3 hat(j) + 6 hat(k)) . Also, find the distnace between these two lines.

Find the equation of the plane passing through the point (1,1,1) and containing the line vec r=(-3hat i+hat j+5hat k)+lambda(3hat i-hat j5hat k) Also,show that the plane contains the lines vec r=(-hat i+2hat j+5hat k)+lambda(hat i2hat j5hat k)

Find the equation of the plane passing through the point (1,1,1) and containing the line vec r=(-3hat i+hat j+5hat k+)lambda(3hat i-hat j-5hat k) Also,show that the plane contains the lines vec r=(-hat i+2hat j+5hat k)+lambda(hat i-2hat j-5hat k)