Question

The unit normal to the plane 2x + y + 2z = 6 can be expressed in the vector form as

Options

• `i3 + j2 + k2`

• `i2/3 + j1/3 + k2/3`

• `i1/3 + j1/2 + k1/2`

• `i1/3 + j1/3 + k2/3`

Answer 1

`i2/3 + j1/3 + k2/3`

Explanation:

Equation of the plane, `2x + y + 2z` = 6

∴ Normal vector, `vecn = (2, 1, 2)`

`|vecn| = sqrt(2^2 + 1^2 + 2^2)` = 3

⇒ Unit normal vector, `hatn = (vecn)/|vecn| = ((2"," 1"," 2))/3`

∴ `hatn = 2/3hati + hatj/3 + 2/3hatk`