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FP3 - Vectors

Hi I was wondering if someone could explain to me the dot product of two vectors and how to go about finding A.B?

I have attached a question which I found, but it doesn't follow the formula of A.B so I was confused as to how to go about these questions and was wondering if someone could explain it??
Reply 1
if

A=a1i+a2j+a3k,B=b1i+b2j+b3k,A.B=(a1b1+a2b2+a3b3)A=a_{1}i+a_{2}j+a_{3}k, B=b_{1}i+b_{2}j+b_{3}k, A.B= (a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3})

https://math.dartmouth.edu/archive/m9f07/public_html/m9lect1031.pdf

the b) and c) are for the cross product and the area of a parallelogram formed by 2 vectors.
(edited 9 years ago)
The formula is: ab=(a1,a2,a3)(b1,b2,b3)=a1b1+a2b2+a3b3\boldsymbol{a} \cdot \mathbf{b}=(a_{1},a_{2},a_{3}) \cdot (b_{1},b_{2},b_{3})=a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}

This is exactly what has happened in part a. So I'm not sure what you mean by it doesn't follow the formula?

Do you mean it doesn't follow: ab=abcosΘ\boldsymbol{a}\cdot \mathbf{b}=|\boldsymbol{a}|| \boldsymbol{b} |cos\Theta
?
(edited 9 years ago)
Original post by rayquaza17
The formula is: ab=(a1,a2,a3)(b1,b2,b3)=a1b1+a2b2+a3b3\boldsymbol{a} \cdot \mathbf{b}=(a_{1},a_{2},a_{3}) \cdot (b_{1},b_{2},b_{3})=a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}

This is exactly what has happened in part a. So I'm not sure what you mean by it doesn't follow the formula?

Do you mean it doesn't follow: ab=abcosΘ\boldsymbol{a}\cdot \mathbf{b}=|\boldsymbol{a}|| \boldsymbol{b} |cos\Theta
?



Yes that's what I meant. It didn't follow the second formula. Am I correct in presuming, that if an angle has not been indicated I use

And when an angle is indicated I use


Sorry this may sound stupid it's just vectors are my least favorite topic in maths!
Original post by Sapphiresmith
Yes that's what I meant. It didn't follow the second formula. Am I correct in presuming, that if an angle has not been indicated I use

And when an angle is indicated I use


Sorry this may sound stupid it's just vectors are my least favorite topic in maths!


That's correct. :smile:

Don't worry, I hated vectors at a level too. Now I'm at uni though, they're one of my favourite things. :biggrin:

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