OP+nOQ = <4,1,-6> + n<2,-7,5> = <4,1,-6> + <2n,-7n,5n> =

<4+2n,1-7n,-6+5n>

Two vectors are perpendicular if and only if their scalar 
(dot)-product is 0, so we set the dot product (OP+nOQ)•OR = 0, 
or 

<4+2n,1-7n,-6+5n>•<3,-2,4> = 3(4+2n)-2(1-7n)+4(-6+5n) =

                                   12+6n-2+14n-24+20n = 0
                                              -14+40n = 0
                                                  40n = 14
                                                    n = 14/40
                                                    n = 7/20

Edwin