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 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.

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 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 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.

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

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 which is at a distance of 5 units fom the origin and perpendiculat to 2hati-3hatj+6hatk

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

The perpendicular distance from the origin to the plane through the point (2,3,-1) and perpendicular to the vector 3hati-4hatj+7hatk is

If a vector 2hati +3hatj +8hatk is perpendicular to the vector 4hati -4hatj + alphahatk, then the value of alpha is