Find the equations of the plane passing through the point (7,8,6) and parallel to the plane ` overset(-) r. (6hati +8hatj +7hatk ) =0`

Find the Cartesian equations of the plane passing through A(7,8,6) and parallel to XY plane.

Find the equation of the plane passing through the point (1,-2,7) and parallel to the plane 5x+4y-11z=6 .

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

(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 and cartesian equation of the line passing through the point P (1,2,3) and parallel to the planes : vec(r).(hati - hatj + 2 hatk) = 5. vec(r).(3hati + hatj + hatk) = 6.

(i) Find the vector equation of the line passing through (1,2,3) and parallel to the planes : vec(r) . (hati - hatj + 2 hatk ) = 5 and vec(r) . (3 hati + hatj + hatk) = 6 . (ii) Find the vector equation of the straight line passing through (1,2,3) and perpendicular to the plane : vec(r) . (hati + 2 hatj - 5 hatk ) + 9 = 0 .

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) .

Find the vector equation of the plane passing through the point (3hati+4hatj+2hatk) and parallel to the vectors (hati+2hatj+3hatk) and (hati-hatj+hatk) .

The equation of plane passing through the point hati+hatj+hatk and paralel to the plane vecr.(2hati-hatj+2hatk)=5 is