Find the equation of the plane passing through the point `hati-hatj+hatk and ` perpendicular to the vectro `3hati-hatj-2hatk` and show that the point `2hati+4hatj` lies on the plane.

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

Find the equation of a line passing through the point (1,2,3) and perpendicular to the plane vecr.(2hati-3hatj+4hatk) = 1 .

Find the vector equation of a line passes through the point hati+3hatj+hatk and parallel to vector 3hati-2hatj+k .

Find the equation of a line passing through the point (2hati-3hatj-5hatk) and perpendicular to the plane vecr.(6hati-3hatj+5hatk) +2=0 . Also find the point of intersection of this line and the plane.

The vector equation of a plane passing through a point having position vector 2hati+3hatj-4hatk and perpendicular to the vector 2hati-hatj+2hatk , is

Find the Cartesian equation of the plane passing through point A(1, 2, 3) and which is perpendicular to a vector vecn=2hati-3hatj+4hatk

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 the point (3,4,-5) and parallel to the vectors 3hati+hatj-hatk and hati-2hatj+hatk .

Find the equation of the plane through the point 2hati+3hatj-hatk and perpendicular to vector 3hati+3hatj+7hatk. Determine the perpendicular distance of this plane from the origin.

Find the equation of a plane passing through origin and which is perpendicular to a normal vector 2hati+ hatj -hatk . (Cartesian form )