Find a unit vector that is orthogonal to both i + j and i + k.

i - j - k

Step-by-step explanation:

Taking the cross product between two vectors will give you a third vector that is orthogonal(perpendicular) to both vectors.

<1,1,0> x <1,0,1>

the determinate of the matrix: <1,-(1),-1>

or: i - j - k