Find the parametric form of vector equation of a line passing through a point `(2,-1,3)` and parallel to line `vec(r)=(hat(i)+hat(j))+t(2hat(i)+hat(j)-2hat(k))`

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

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 parametric form of vector eqution of the straight line passing through (-1,2,1) and paralle to the straight line vec(r)=(2hat(i)+3hat(j)-hat(k))+t(hat(i)-2hat(j)+hat(k)) and lines find the shortest distance between the lines.

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 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 equations of a line passing through the point P(2,-1,3) and perpendicular to the lines vec(r ) =(hat(i) + hat(j) -hat(k)) +lambda (2hat(i) -2hat(j) +hat(k)) and vec( r) =(2hat(i) -hat(j) -3hat(k)) +mu (hat(i) +2hat(j) +2hat(k))