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

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

Quote:

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 $\displaystyle \overrightarrow{AQ}$ and $\displaystyle \overrightarrow{AB}$ are not collinear.