Find the equation of the plane passing through (a,b,c) and paralle toteh plne `vecr.(hati+hatj+hatk)=2`.

(i) Find the equations of the plane passing through (a,b,c) and parallel to the plane vec(r) . (hati + hatj + hatk) = 2 . (ii) Find the vector equation of the plane through the point hati + hatj + hatk and parallel to the plane vec(r). (2 hati - hatj + 2 hatk) = 5 .

Find the vector equation o the line passing through (1,2,3) and parallel to the planes vecr.(hati+hatj+2hatk)=5 and vecr.(3hati+hatj+hatk)=6

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes vecr*(hati-hatj+2hatk)=5 and vecr*(3hati+hatj+hatk)=6 .

Find vector equations of the plane passing through A(-2,7,5) and parallel to vectors 4 hati -hatj +3hatk and hati +hatj -hatk .

Find the equation of the plane passes through the point (2,1,-2) and parallel to the plane vecr.(3hati+hatj-hatk) = 0 .

Find the equation of the plane through (3,4,-1) which is parallel to the plane vecr.(2hati-3hatj+5hatk)+7=0

Find the equation of the plane passing through the intersection of the planes vecr.(2hati+hatj+3hatk)=7 , vecr.(2hati+5hatj+3hatk)=9 and the point (2,1,3) .

Find the equation of the plane passing through the intersection of the planes vecr.(2hati+hatj+3hatk)=7, vecr.(2hati+5hatj+3hatk)=9 and the point (3,2,-1) .

Find the equation of the plane through the point (3,4,-1) and parallel to the plane vecr.(2hati-3hatj+5hatk)+7=0

Find the vector and Cartesian equations of the plane passing through the point (1,2,-4) and parallel to the lines vecr=(hati+2hatj+hatk)-lambda(2hati+3hatj+6hatk) and vecr=(hati-3hatj+5hatk)+mu(hati+hatj-hatk) .