(1) Because BB 1C is a diamond, B 1C is perpendicular to BC 1C, and because AO is perpendicular to B 1C, B1c is perpendicular to the plane OBA.

(2) tetrahedral volume abcb1:1/3 * s △ bb1c * ao =1/3 * s △ ABC * b1Distance to the plane ABC. S △ Ab 1C = SQRT (3)/4，S △ ABC = SQRT (7)/8。 Therefore, the distance from B 1 to plane ABC is 2*sqrt(2 1)/7.