The given answer does not even lie on the line OB. So either you have misread the question, or the book is wrong.
Given A(1,7) and B(8,3). C lies on OB where O is the origin. If vector OA + BA + CA is perpendicular to vector OB, find the coordinates of C.
The answer i get is C=(112/73 , 42/73) but the answer given is (-71/2 , 195/7). What answer do you get?
Maybe i should show my steps and someone can point out my mistake for me...
C lies on OB, so C = k(8,3)
BA = OA-OB = (-7,4)
CA= OA-OC = (1-8k, 7-3k)
OA + BA + CA = (-5-8k, 18-3k)
OA + BA + CA is perpendicular to vector OB, so
OA + BA + CA . OB = 0
(-5-8k, 18-3k) . (8,3)=0
-8(5+8k) + 3(18-3k) = 0
So C = k(8,3) = 14/73 . (8,3)
Which step have i go wrong?