If b is in the plane spanned by a1 and a2, then there is no orthogonal projection of b onto a1 and a2 (in other words, you can't draw a perpendicular line down from b to the plane spanned by a1 and a2).
Since two vectors are given here, we can assume that the plane passes through the origin (else the problem would have to specify points). The cross product of a1 and a2 is (-8, 3, 4) (I do not wish to type this out here. Feel free to contact me on how I got this if you need to do this by hand). So that means that the dot product of (-8,3,4) with a1 and a2 are 0. And since the plane goes through the origin, as mentioned before, we can write the equation of the plane as
-8(x - 0) + 3(y - 0) + 4(z - 0) = 0, so -8x + 3y + 4z = 0.
Now, we can plug in b into this equation to see which value(s) of h would make it lie in the plane:
-8(5) + 3(8) + 4(h) = 0 -> -40 + 24 + 4h = 0 -> -16 + 4h = 0 -> 4h = 16 -> h = 4.
Thus, h = 4 would make it lie in the plane.
