Find the values of p so that the lines `(1-x)/3=(7y-14)/(2p)=(z-3)/2`and `(7-7x)/(3p)=(y-5)/1=(6-z)/5`are at right angles.

Explanation

First line `(1-x)/(3) = (7y-14)/(2p) - (z-3)/(2)`
`rArr (x-3)/(-3) = (y-2)/((2p)/(7)) = (z-3)/(2) "……"(1)`
and second line `( 7-7x)/(3p) = (y-5)/(1) = (6-z)/(5)`
`rArr (x-1)/((-3p)/(7)) = (y-5)/(1)= (z-6)/(-5) "….."(2)`
For perpendicular lines for the (1) and (2)
`-3((-3p)/(7)) + (2p)/(7)(1)+2(-5) = 0`
`rArr (9p)/(7) + (2p)/(7) - 10 = 0`
`rArr p = (70)/(11)`