[" Find the vector and Cartesian equations of the plane containing the two lines "],[vec r=2hat imath+hat jmath-3hat k+lambda(hat imath+2hat jmath+5hat k)" and "vec r=3hat imath+3hat jmath+2hat k+mu(3hat imath-2hat jmath+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 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 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=(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 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 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 equations of the line through the point (1,2,4) and perpendicular to the two lines.vec r=(8hat i-19hat j+10hat k)+lambda(3hat i-16hat j+7hat k) and vec r=(15hat i+29hat j+5hat k)+mu(3hat i+8hat j-5hat 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

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 vector and cartesian equations of the line through the point (1,2,-4) and perpendicular to the two lines- vec r=(8hat i-19hat j+10hat k)+lambda(3hat i-16hat j+7hat k) and vec r=(15hat i+29hat j+5hat k)+mu(3hat i+8hat j-5hat k)

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)