Hello, Vector assistance required

Hello, I wish you happiness and well-being.

I require some help with vectors, it is about forming vector equations.

The points A and B have position vectors (5i + j − 2k) and (6i − 3j + k) respectively.

We are told to form a vector equation using this equation by finding AB.

I have formed two vector equations:
(1) 5i+i-2k + s(i-4j+3k)
(2) 6i-3j+k + s(i-4j+3k)

I would have thought that both equations are acceptable considering the line passes both A and B.

However, in many textbooks and answer sheets I have seen only 1 equation being used (primarily of point A.) Will I be penalised for stating 2 equations or is there a method in finding the correct vector equations.

The correct answer here seems to be r = (5i + j − 2k) + s(i − 4j + 3k) why is it not the other?

Many thanks.

Relax, there are infinitely many correct answers.

Thank you for the reply.

Does this mean I can state both vector equations and use either in the extending questions (part b or c etc)?

Just one correct equation will do. Don't forget to write r =...