[" Find the vector and cartesian equations of a "],[" plane containing the two lines "],[vec r=2hat i+hat j-3hat k+lambda(hat i+2hat j+5hat k)" and "],[vec r=3hat i+3hat j+2hat k+mu(3hat i-2hat j+5hat k)],[" Also show that the line "],[vec r=(2hat i+5hat j+2hat k)+p(3hat i-2hat j+5hat k)" lies in the "]

Find the vector and Cartesian equations of the plane containing the two lines vec r=2hat i+hat j-3hat k+lambda(hat i+2hat j+5hat k) and vec r=3hat i+3hat j+2hat k+mu(3hat i-2hat j+5hat k)

Find the vector and cartesian equation of the plane containing the two lines vec(r)=2hat(i)+hat(j)-3hat(k)+lamda(hat(i)+2hat(j)+5hat(k)) and vec(r)=3hat(i)+3hat(j)-7hat(k)+mu(3hat(i)-2hat(j)+5hat(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)

If vec r=(hat i+2hat j+3hat k)+lambda(hat i-hat j+hat k) and vec r=(hat i+2hat j+3hat k)+mu(hat i+hat j-hat k) are bisector of two lines is

Find the vector and cartesian equations of a plane containing the two lines vec(r) = (2 hat(i) + hat(j) - 3 hat(k)) + lambda(hat(i) + 2 hat(j) + 5 hat(k)) and vec(r) = (3hat(i) + 3 hat(j) + 2 hat(k)) + lambda (3 hat(i) - 2 hat(j) + 5 hat(k)) . Also show that the line vec(r) = (2 hat(i) + 5 hat(j) + 2 hat(k)) + p (3 hat(i) - 2 hat(j) + 5 hat(k)) lies in the plane.

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=(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)

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)+u(2hat i+4hat j-5hat k)

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

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