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

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SUMMARY

The discussion centers on finding the position vector Q on line segment AB in R3, where A has coordinates (7, -2, 3) and B has coordinates (1, -5, 0). The correct calculation of Q, which is located at AQ = 2/3 AB, leads to the position vector Q being (3, -4, 1). This result contradicts the book's answer of (2, -3, -1). The consensus in the discussion confirms that the user's calculations are accurate, indicating a potential error in the book's solution.

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Homework Statement


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

Homework Equations


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

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
 
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