Find the Cartesian as well as vector equations of the planes through the intersection of the planes ` -> rdot(2 hat i+6 hat j)+12=0\ a n d\ -> rdot(3 hat i- hat j+4 hat k)=0` which are at a unit distance from the origin.

Options

A. `vecr.(2hati+hatj+2hatk)+3=0`
B. `vecr.(hati-2hatj+2hatk)+3=0`
C. `vecr.(hati-2hatj-2hatk)+3=0`
D. `vecr.(2hati+hatj+2hatk)-3=0`

Answer

A

Explanation

The equation of the through the intersection of the given planes is
`{vecr.2hati+6hatj+12}+lamda{vecr.3hati-hatj+4hatk}=0`
or `vecr.{(2+3lamda)hati+(6-lamda)hatj+4lamda hatk+12}=0`……………i
It is at a unit distance from the origin
`:.|12/(sqrt((2+3lamda)^(2)+(6-lamda)^(2)+16lamda^(2)))|=1implieslamda=+-2`
Hence the equations of required planes are
`vecr.(2hati+hatj+2hatk)+3=0` and `vecr.(hati-2hatj+2hatk)-3=0`