equation of the plane containing the lines ` (i+2j -k)+ s(i+j+3k) is

Equation of the plane containing the lines vec(r )= vec(i) + 2vec(j) -vec(k) + lamda (vec(i) + 2vec(j)-vec(k)), vec(r )=vec(i) + 2vec(j) -vec(k)+ mu (vec(i) + vec(j) + 3vec(k)) is

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

Equation of the plane containing the line vec r = i+j + lambda (2i+j+4k) is

Equation of the plane containing the line (x+2)/5 = (y-3)/-1 = (z+1)/1 , and perpendicular to the plane barr.(i+j-k)=-3 is

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 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 parametric form of vector equation, and Cartesian equations of the plane containing the line vec(r)=(hat(i)-hat(j)+3hat(k))+t(2hat(i)-hat(j)+4hat(k))" and perpendicular to plane "vec(r)*(hat(i)+2hat(j)+hat(k))=8.

The vector equation of the plane passing through the points i + 2j + 5k, -5j + k, -3i + 5j is

A : The vector equation of the plane passing through the point 2i + 2j - 3k and parallel to the vectors 3i + 3j - 5k, i + 2j + k is r = 2i + 2j - 3k + s(3i + 3j - 5k) + t(i + 2j + k) R : The vector equation of the plane passing through the points a, b, c is r = (1 - s - t) a + sb + tc