Find the normal vector to the plane 4x + 2y + 3z – 6 =0

Find the unit normal vectors to the plane 2x+y-2z=5 .

The unit normal vector to the plane 2x - y + 2z = 5 are …………..

The unit normal vector to the plane 2x + 3y + 4z =5 is ………….

Equation to the two planes are 2x+y-2z=5 and 3x-6y-2z=7 i.Find the normal vectors to these planes ii. Find the angle between these two planes.

Find the equation of the plane through the intersection of the planes 2x - 3y + z - = 0 and x - y + z + 1 = 0 and perpendicular to the plane x + 2y - 3z + 6 = 0.

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

Find the direction cosines of the normal to the plane 12x + 3y - 4z = 65. Also, find the non-parametric form of vector equation of a plane and the length of the perpendicular to the plane from the origin.

Find the equation of the plane containing the line of intersection of the planes x + y + z - 6 = 0 and 2x + 3y + 4z + 5 = 0 and passing through the point (1,1,1)

Find the vector and Cartesian equations of the plane passing through the point (1,1,-1) and perpendicular to the planes x + 2y + 3z - 7 = 0 and 2x - 3y + 4z = 0