The equation of line passing through `(3,-1,2)` and perpendicular to the lines `vec(r)=(hat(i)+hat(j)-hat(k))+lamda(2hat(i)-2hat(j)+hat(k))` and `vec(r)=(2hat(i)+hat(j)-3hat(k))+mu(hat(i)-2hat(j)+2hat(k))` is

Find the equation of the straight line passing through the point (2,-1,3) and perpendicular to the lines vec(r)=(hat(i)+hat(j)-hat(k))+lamda(2hat(i)+hat(j)-3hat(k)) and vec(r)=(hat(i)-hat(j)-hat(k))+mu(hat(i)+hat(j)+hat(k)) .

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))

A line passes through (2,-1,3) and perpendicular to the lines vec(r)=(hat(i)+hat(j)+hat(k))+lamda(2hat(i)-2hat(j)+hat(k)) and vec(r)=(2hat(i)-hat(j)-3hat(k))+mu(hat(i)+2hat(j)+2hat(k)) . Obtain its vector equation.

vec(r )=(-4hat(i)+4hat(j) +hat(k)) + lambda (hat(i) +hat(j) -hat(k)) vec(r)=(-3hat(i) -8hat(j) -3hat(k)) + mu (2hat(i) +3hat(j) +3hat(k))

Find the shortest distance between the lines vec(r)=(hat(i)+2hat(j)+hat(k))+lamda(hat(i)-hat(j)+hat(k)) and vec(r)=2hat(i)-hat(j)-hat(k)+mu(3hat(i)-hat(j)+hat(k))

Show that the lines vec(r) =(hat(i) +2hat(j) +hat(k)) +lambda (hat(i)-hat(j)+hat(k)) " and " vec(r ) =(hat(i) +hat(j) -hat(k)) + mu (hat(i)- hat(j) + 2hat(k)) Do not intersect .

Find the equation in vector and cartesian form of the line passing through the point : (2,-1, 3) and perpendicular to the lines : vec(r) = (hat(i) + hat(j) - hat(k)) + lambda (2 hat(i) - 2 hat(j) + hat(k)) and vec(r) = (2 hat(i) - hat(j) - 3 hat(k) ) + mu (hat(i) + 2 hat(j) + 2 hat(k)) .