Why not just write it in? It's not that difficult. The given vector is <5, -24, 50> and the plane is [tex]x= \lambda<4, 5, 2>+ \mu<-5, 5, 3>+ <5, 2, -2>.

Is the vector parallel to the plane? Are there values for and such that ?

Is the vector in the plane? What does that mean? A vector is "movable" and does not actually lie inanyplane. Are you interpreting <5,-24,50> as the vector from (0, 0, 0) to (5, -24, 50)? If so are there values for and such thatandare there values for and such that ?