It is known that a, B and C are not collinear, and a point m outside the plane ABC satisfies the vector om = 1 / 3 vector OA + 1 / 3 vector ob + 1 / 3 vector OC It is known that a, B and C are not collinear, and a point m outside the plane ABC satisfies the vector om = 1 / 3 vector OA + 1 / 3 vector ob + 1 / 3 vector OC (1) Judge whether the three vectors Ma, MB and MC are coplanar; (2) Judge whether point m is in plane ABC

It is known that a, B and C are not collinear, and a point m outside the plane ABC satisfies the vector om = 1 / 3 vector OA + 1 / 3 vector ob + 1 / 3 vector OC It is known that a, B and C are not collinear, and a point m outside the plane ABC satisfies the vector om = 1 / 3 vector OA + 1 / 3 vector ob + 1 / 3 vector OC (1) Judge whether the three vectors Ma, MB and MC are coplanar; (2) Judge whether point m is in plane ABC

(1) Coplanar proof: ∵ 1 / 3 + 1 / 3 + 1 / 3 = 1 ∵ m, a, B, C four points coplanar ∵ vector Ma, vector MB, vector MC three vectors coplanar note: the necessary and sufficient condition of four points coplanar is x + y + Z = 1 (2) four points coplanar, m naturally in the plane ABC, maybe this problem is not so proof that it wants to do so (1) vector om = 1 / 3, vector OA + 1 / 3 direction