Find the vector and Cartesian equation of the plane that passes through the point (1,4,6) and the normal vector to the plane is `hati-2hatj+hatk`.

Find the vector and Cartesian equation of the plane that passes throgh the point (1,0,-2) and the normal vector to the plane is hati+hatj-hatk.

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

Find the vector and cartesian equations of the planes : (a) that passes through the point (1,0,-2) and the normal to the plane is hati + hatj - hatk (b) that passes through the point (1,4,6) and the normal vector of the plane is hati - 2 hatj + hatk .

Find the vector and cartesian equations of the planes (a) that passes through the point (1,0,-2) and the normal to the plane is (b) that passes through the point (1,4,6) and the normal vector to the plane is the normal vector to the plane is the normal vector to the plane is hat i-2hat j-hat k

Find the vector and cartesian equations of the plane that passes through the point (0, 1, -2) and normal to the vector hati + hatj + hatk .

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.

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 and cartesian equation of plane which passes through the point (1,3,-2) and normal to the vector (2hati+hatj-2hatk) .

Find the vector and cartesian equation of the plane : (i) that passes through the point (5,2,-4) and perpendicular to the line with direction-ratios lt 2, 3, -1 gt (ii) that passes through the point (1,0, -2) and the normal to the plane is hati + hatj - hatk (iii) that passes through the point (1,4,6) and the normal vector to the plane is hati - 2 hatj + hatk .