Question

The equation of the plane through (-1, 1, 2), whose normal makes equal acute angles with co-ordinate axes is ______ 

Options

• `overliner.(hati + hatj + hatk) = 2`

• `overliner.(hati + hatj + hatk) = 6`

• `overliner.(3hati - 3hatj + 3hatk) = 2`

• `overliner.(hati - hatj + hatk) = 3`

Answer 1

The equation of the plane through (-1, 1, 2), whose normal makes equal acute angles with co-ordinate axes is `underline(overliner.(hati + hatj + hatk) = 2)`

Explanation:

Let A ≡ (-1, 1, 2)

∴ `overlinea = -hati + hatj + 2hatk`

`overlinen = hati + hatj + hatk`

∴ equation of plane is `overliner.overlinen = overlinea.overlinen`

⇒ `overliner.(hati + hatj + hatk) = (-hati + hatj + 2hatk).(hati + hatj + hatk)`

⇒ `overliner.(hati + hatj + hatk) = 2`