Question

Reduce the equation `barr*(3hati - 4hatj + 12hatk)` = 3 to the normal form and hence find the length of perpendicular from the origin to the plane.

Answer 1

Given equation is `barr*(3hati - 4hatj + 12hatk)` = 3 

This is of the form `barr*barn` = 3

∴ `barn = 3hati - 4hatj + 12hatk`

∴ `|barn| = sqrt((3)^2 + (-4)^2 + (12)^3`

= `sqrt(9 + 16 + 144)`

= `sqrt(169)`

= 13

Now `barr*barn` = 3 can be written as

`barr*barn/|barn| = 3/|barn|`

∴ `barr*((3hati - 4hatj + 12hatk))/13 = 3/13`

This is the normal form of the equation of given plane.

Length of perpendicular from the origin to the plane is `3/13`