Find the vector equation of a lane passing through a point having position vector `2i+3j-4k` and perpendicular to the vector `2i-j+2kdot` Also, reduce it to Cartesian form.

Explanation

We know that,

`(r−a)⋅n=0`

i.e.`r⋅n=a⋅n`


`r⋅(2−j​+2k)=(2i+3j−4k)⋅(2i−j​+2k)`

`=>r⋅(2i−j​+2k)=4−3−8`

`=>r⋅(2i−j​+2k)=−7`