Can someone please explain how you find the answer. I don’t understand how you find it with a length

Question

Find a vector in R3 that has length 5 and is orthogonal to both a=[2 1 -3] and b=[1 -2 1]

Answer 1

Let vectr x = [m n p]. Then because of ortogonality: x·a = 2m + n - 3p = 0 (1) , x·b = m - 2n + p = 0 (2)

m² + n² + p² = 25 (3). Fro (1) and (2): 5m - 5p = 0; m = p; n = p. Then from (3): 3p² = 25; p = ±5√3/3.

So, we have 2 vectors: x₁ = [5√3/3 5√3/3 5√3/3]; x₂ = [-5√3/3 -5√3/3 -5√3/3]