Thread: Questions about Dot Product (Vectors)

This is my first post here so I'm sorry if this isn't the right section (didn't see a vectors subforum). I am also not sure how to put arrows on top of letters, so assume that every letter in the following question is a vector. I will also use | | for magnitude.

1. |a| = 3 , |b| = 2 , the angle in between these vectors is 60
Determine the numerical value of (3a + 2b) dot (4a - 3b). - In order to do this I tried distributing.

I know that (3a dot 4a) = 12|a|² and (2b dot -3b) = -6|b|²
I however don't know what to do in the case of (3a dot -3b) and (2b dot 4a)

The formula given is ( |a||b|cosθ = a dot b ) and the final answer is 81 as listed in the back of the book.


2. A regular hexagon has sides of 3cm, as shown below. Determine a dot b.



This is my drawing - I slid b over resulting in an angle of 120 between a and b.
I used the above formula to yield: |3||3|cos120 = -4.5

The answer in the back of the book is however 4.5 (positive, not negative). This has also occurred in other questions where I am getting negative answers where they should be positive - is there something I'm not doing right?

All help would be greatly appreciated.

Originally Posted by StuckOnVectors

1. |a| = 3 , |b| = 2 , the angle in between these vectors is 60
Determine the numerical value of (3a + 2b) dot (4a - 3b). - In order to do this I tried distributing.

I know that (3a dot 4a) = 12|a|² and (2b dot -3b) = -6|b|²
I however don't know what to do in the case of (3a dot -3b) and (2b dot 4a)

The formula given is ( |a||b|cosθ = a dot b ) and the final answer is 81 as listed in the back of the book.

So, roughly speaking (!), we have
after distributing.
"a" = 3, "b" = 2, and "ab" = 3 by following Plato's computation.

I'm still just not understanding.. How did you come up with -ab = -3? I know that you have to use the formula, I just don't get how.

Originally Posted by StuckOnVectors

2. A regular hexagon has sides of 3cm, as shown below. Determine a dot b.

This is my drawing - I slid b over resulting in an angle of 120 between a and b.
I used the above formula to yield: |3||3|cos120 = -4.5

The answer in the back of the book is however 4.5 (positive, not negative). This has also occurred in other questions where I am getting negative answers where they should be positive - is there something I'm not doing right?

All help would be greatly appreciated.

The vectors including an angle had to be placed tail to tail and not - as you did - head to tail. Or in other words: The arrows representing vectors had to start at the vertex of the angle.

earboth thank you for the help, I see where I went wrong with the hexagon

thechaz the problem was that I didn't know how to get to , but i figured it out

anyone reading this: is the same thing as - not knowing this was my problem