Doing cross product ofwhattwo vectors? You are only given one vector. Any vector, <x, y, z>, perpendicular to <1, -1, 5> must satisfy x- y+ 5z= 0 (their dot product is 0). Solve that for x: x= y- 5z.

So <x, y, z>= <y- 5z, y, z>= <y, y, 0>+ <-5z, 0, z>= y<1, 1, 0>+ z<-5, 0, 1>.

Now, what are two vectors that are perpendicular to <1, -1, 5>? Are they independent?