Three aircraft (called A, B, and C) are positioned in space; the position of each aircraft is specified by three space coordinates (x,y,z), given with respect to the space station having coordinates (0,0,0). Aircraft A has fixed position (2, 5, 8), and aircraft B has fixed position (3, 5, 8).

Writ a and b for the 3-dimensional vectors pointing from the space station to A and to B, respectively. Do the following.

a) Determine the distance between aircraft A and B.

b) You want to place aircraft C such that the distance between B and C is the same as the distance between B and A, and such that the line through B and C is orthogonal to the line through B and A. Determine the set of all possible coordinates (c1, c2, c3) of C. Hint: your answer should be a set of triples (c1, c2, c3) that satisfy certain explicit equations.

Three aircraft (called A, B, and C) are positioned in space; the position of each aircraft is specified bythree space coordinates (LB, 3;, 2), given with respect to the space station having coordinates (0,0,0). Aircraft A has xed position (2, 5, 8), and aircraft B has xed position (3, 5, 8). Write a. and b for the 3-dimensional vectors pointing from the space station to A and to B, respectively. Do the following. a) Determine the distance between aircraft A and B. b) You want to place aircraft C such that the distance between B and C is the same as the distance between B and A, and such that the line through B and C is orthogonal to the line through B and A. Determine the set of all possible coordinates (C1, 62, C3) of C. Hint: your answer should be a set of triples (C1, 62, C3) that satisfy certain explicit equations