# Math Help - Easy Ratio Vector Question, but not sure if answer is wrong

1. ## Easy Ratio Vector Question, but not sure if answer is wrong

Let A, B be points in R3 with position vectors

a (7,-2,3)
b (1,-5,0)

Let Q be the point on AB such that AQ= 2/3 AB
Find q, the position vector of Q

2. Relevant equations
The back of the book says the answer is: (2,-3,-1)

3. The attempt at a solution
First, I found the vector of AB: (-6,-3,-3)
So Q should be: a+(2/3)(AB)
ie: (7,-2,3)+(-4,-2,-2)
=(3,-4,1)
Which is different to the answer given by the book.
Did i do anything wrong?
Thanks

2. ## Re: Easy Ratio Vector Question, but not sure if answer is wrong

Originally Posted by geoff18
Let A, B be points in R3 with position vectors

a (7,-2,3)
b (1,-5,0)

Let Q be the point on AB such that AQ= 2/3 AB
Find q, the position vector of Q

2. Relevant equations
The back of the book says the answer is: (2,-3,-1) <-- that's definitely wrong

3. The attempt at a solution
First, I found the vector of AB: (-6,-3,-3)
So Q should be: a+(2/3)(AB)
ie: (7,-2,3)+(-4,-2,-2)
=(3,-4,1)
Which is different to the answer given by the book.
Did i do anything wrong?
Thanks
The vectors $\overrightarrow{AQ}$ and $\overrightarrow{AB}$ are not collinear.