Hello; 1. The problem statement, all variables and given/known data "The point C lies between A and B and is 5 units from A. OA = 2i + 3j OB = -4i - 5j Find OC." 2. Relevant equations Pythagoras' Theorem 3. The attempt at a solution This is not exactly a homework question since this is independent study, but I was wondering why I couldn't get the same answer as my textbook unless my textbook is wrong - but if it isn't, then that means I haven't grasped this topic yet. First find the vector AB; AB = OB - OA AB = -4i - 5j - 2i - 3j = -6i - 8j The magnitude of AB is therefore 10, by Pythagoras' Theorem. Since C is 5 units from A and lies between A and B; AC = (AB)/2 AC = 0.5(-6i - 8j) = -3i - 4j To find OC, we simply substitute values into the equation OA + AC = OC; OA + AC = OC 2i + 3j - 3i - 4j = -i - j = OC So OC should be -i - j, but I don't see the error I have made... my textbook says it should be 0.8i + 1.4j. This problem has been bugging me because I thought I understood this, perhaps there is something deeper I haven't noticed/considered? Thanks.
Hello FeDeX_LaTeX! Your method looks correct to me. Perhaps the question should say 2 units instead of 5 ?
Hello; Thank you for the quick reply! I did the problem again assuming it was 2 units from A, not 5, and I did indeed get the textbook's answer. But the problem does say 5 units. I suppose it is just a typo. Thanks! Now just one more topic and I've finished this chapter.