= & gtm^2+n^2 = 1 ( 1)

OA。 OC = |OA||OC|cos(π/4)

(m，n，0)。 ( 1, 1, 1) = 1.√3 ( √2/2)

m+n = √6/2 (2)

Sub (2) becomes (1)

m^2 +(√6/2-m)^2 = 1

4m^2 - 2√6m + 1 =0

M = (√6 +√2)/4 or (√6 -√2)/4.

When m= (√6 +√2)/4, n= (√6 -√2)/4.

When m= (√6 -√2)/4, n= (√6 +√2)/4.

OA =(√6 +√2)/4, (√ 6-√ 2)/4,0) or (√ 6-√ 2)/4,0)

Similarly,

Died in OC = |OB||OC|cos(π/4)

(0，n，p)。 ( 1, 1, 1) = 1.√3 (√2/2)

n+p = √6/2

p = √6/2 - n

When n = (√6 -√2)/4, p=(√6 +√2)/4.

When n = (√6 +√2)/4, p=(√6 -√2)/4.

OB =(0, (√6 -√2)/4, (√6 +√2)/4) or (0, (√6 +√2)/4)