if you could answer
i, iii, iv vi, vii (with annotation)
thank you
Extracted text: Let A, B, C be distinct points in 3-space with position vectors a, b, c respectively. Suppose that A, B, C do not all lie on the same line, and let M be the plane passing through the three points A, B, C. Assume that M does not pass through the origin. Let D be the point on the line segment AB such that |AD |=(1/3)|AB→| Let d be the position vector of D. Determine which equates to what answer: i. ((b-a) x (c- a) - (b- c) ii. 2b ii. r. (b- a) 3Dа: (b- a) iv. (a + 2b)/3 v. ax (b· c) vi. (r-а) . ((d- а) х (с-а)) — 0 vii. (2a +b)/3 viii. (a+b+ c)/3 іx. (а + с)/2 х. a. a answers: (is a real number greater than 0), (is the position vector of the midpoint of the line segment AC), (is the position vector of a point that lies on the plane M but does not lie on any of the line segments AB, AC or BC), (is a meaningless expression), (is the position vector of a point not lying on the plane M), (is a vector equation for a plane that passes through A but not through B), (is a real number less than 0), (is a vector equation for the plane M), (is the position vector of D), (is the position vector of A), (equals the real number 0), (is the position vector of the midpoint of the line segment DB)