Let a→,b→ and c→ be three non-coplanar vectors and d→ be a non-zero vector, which is perpendicular to (a→+b→+c→). Now d→=(a→×b→)sin⁡x+(b→×c→)cos⁡y+2(c→×a→) . then

d→⋅a→=[a→b→c→]cos⁡y=−d→⋅(b→+c→) or  cos⁡y=−d→⋅(b→+c→)[a,→b→,c→] Similarly, sin⁡x=d→⋅(a→+b→)[a→b→c→] and d→⋅(a→+c→)[a→b→c→]=−2∴ sin⁡x+cos⁡y+2=0 or  sin⁡x+cos⁡y=−2 or  sin⁡x=−1,cos⁡y=−1Since we want the minimum value of x2 + y2 , x=−π/2,y=πminimum value of x2+y2 is 5π2/4