# Thread: Dot product of 2 vectors

1. ## Dot product of 2 vectors

Given a and b are unit vectors, if the angle between them is 60, determine $\displaystyle (6a + b) \cdot (a - 2b)$

I have no idea how to do it. Plugging it in to the standard formula where 60 is the angle does not give the correct answer.

2. ## Re: Dot product of 2 vectors

If a is a UNIT vector, what does tha make $\displaystyle a\cdot a$?

If a and b have a 60º angle between them, what does tha make $\displaystyle a\cdot b$? Something to do with a cosine.

3. ## Re: Dot product of 2 vectors

$\displaystyle a \cdot a = 1$

I still don't get it.

4. ## Re: Dot product of 2 vectors

for vectors a,b:

$\displaystyle cos(\theta) = \frac{a \cdot b}{|a||b|}$

if a and b are unit vectors, |a| = |b| = 1.

since the angle between a and a is 0, that should give you a big hint on what $\displaystyle a \cdot a$ is.

5. ## Re: Dot product of 2 vectors

Originally Posted by chengbin
Given a and b are unit vectors, if the angle between them is 60, determine $\displaystyle (6a + b) \cdot (a - 2b)$

I have no idea how to do it. Plugging it in to the standard formula where 60 is the angle does not give the correct answer.
Well,

expand by respective dot product (6a+b)(a-2b)

Pretty much like the normal numbers expansion ( Keep it ordered though )

Then a(dot)a=1
b(dot)b=1
a(dot)b=lengtha * lengthb * cos60

but a, b unit vectors with 1 unit lengths each

Proceed ...

Good Luck.

PS: Wherever you come to let us say

6a(dot)b =6(a(dot)b) can take the constant coeff. out,

a(dot)b=[b (dot) a]=you know what !