Findt the vector equation of the plane passing through the intersection of the planes `r*(2hat(i)+2hat(j)-3hat(k))=7, r*(2hat(i)+5hat(j)+3hat(k))=9` and through the point (2, 1, 3).

Find the magnitude of the vector (2hat(i) - 3hat(j) - 6hat(k)) + (-hat(i) + hat(j) + 4hat(k)) .

Find the Cartesian equation of the following planes: r.(hat(i)+hat(j)-hat(k))=0

Find the Cartesian equation of the following planes: r.(2hat(i)+3hat(j)-4hat(k))=1

Find the equation of the plane passing through the point P(1,1,1) and containing the line vec(r) = (-3 hat(i) + hat(j) + 5 hat(k)) + lambda (3 hat(i) - hat(j) - 5 hat(k)) . Also, show that the plane contains the line vec(r) = (- hat(i) + 2 hat(j) + 5hat(k)) + mu (hat(i) - 2 hat(j) - 5 hat(k)) .

Find the angle between the planes whose vector equation are r.(2hat(i)+2hat(j)-3hat(k))=5, r.(3hat(i)-3hat(j)+5hat(k))=3 .

Find the equation of the line which passes through the point (1,2,3) and is parallel to the vector 3hat(i)+2hat(j)-2hat(k) .

Find the vector and Cartesian equations of the planes. That passes through the point (1, 4, 6) and the normal to the plane is hat(i)-2hat(j)+hat(k) .