Find the vector and cartesian equation 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 = (3 hat 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 plane.

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

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 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 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))

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 (S.D.) between the lines : vec r = hat i + hat j + lambda (2 hat i- hat j + hat k) and vec r = 2 hat i + hat j- hat k + mu (3 hat i - 5 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)

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)

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)

Equation of the plane containing the lines vec r=(hat i-2hat j+hat k)+t(hat i+2hat j-hat k)vec r=(hat i+2hat j-hat k)+s(hat i+hat j+3hat k) is