If the line `barr = (hati - 2hatj + 3hatk) + lambda(2hati + hatj + 2hatk)` is parallel to the plane `barr *(3hati - 2hatj + phatk)` find the value of p.

Explanation

The line `barr = bara + lambdabarb` and the plane `barr.barn = p` are parallel , if `barb.barn =0`
Here, `barb = 2hati + hatj + 2hatk `and `barn =3hati - 2hatj + phatk`
Since , given line is parallel to plane , so
`therefore " "barb. barn = (2hati + hatj + 2hatk).(3hati - 2hatj + phatk) = 0`
`rArr 2(3) +1(-2) +2(p) =0`
` 6-2+2p =0`
`2p = - 4`
`rArr" " p = - 2`