i. The given equation of the plane is 2x – y + 2z = 8

This is in Cartesian form, to convert this to vector form, this can be done as shown below:

We know

Hence the above equation becomes,

The vector equation of the plane whose Cartesian form 2x – y + 2z = 8 is given is

ii. x + y – z = 5

This is in Cartesian form, to convert this to vector form, this can be done as shown below:

We know

Hence the above equation becomes,

The vector equation of the plane whose Cartesian form x + y – z = 5 is given is

iii. x + y = 3

This is in Cartesian form, to convert this to vector form, this can be done as shown below:

We know

Hence the above equation becomes,

The vector equation of the plane whose Cartesian form x + y =3 is given is