Given :

Equations of plane are :

4x + 11y + 2z + 3 = 0

3x – 2y + 5z = 8

To Prove : are perpendicular.

Formula :

1) Dot Product :

If are two vectors

then,

Note :

Direction ratios of the plane given by

ax + by + cz = d

are (a, b, c).

For plane

4x + 11y + 2z + 3 = 0

direction ratios of normal vector are (4, 11, 2)

therefore, equation of normal vector is

And for plane

3x – 2y + 5z = 8

direction ratios of the normal vector are (3, -2, 5)

therefore, the equation of normal vector is

Now,

= 12 – 22 + 10

= 0

Therefore, normals to the given planes are perpendicular.