# Vector Dot Product question

## Homework Statement

Expand and simplify:
(2$$\vec{a}$$ + 3$$\vec{b}$$) .(5$$\vec{a}$$ - $$\vec{b}$$

## The Attempt at a Solution

I tried expanding it, but was a little confused, and would really appreciate any help..would it be (2$$\vec{a}$$)($$\vec{a}$$) = 2 $$\vec{a}$$2?

Thanks..

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Mark44
Mentor

## Homework Statement

Expand and simplify:
(2$$\vec{a}$$ + 3$$\vec{b}$$) .(5$$\vec{a}$$ - $$\vec{b}$$

## The Attempt at a Solution

I tried expanding it, but was a little confused, and would really appreciate any help..would it be (2$$\vec{a}$$)($$\vec{a}$$) = 2 $$\vec{a}$$2?

Thanks..
As your final answer? No. The dot product has a bunch of properties, some of which apply in this problem.

like 10 a 2 - 3 b2

now im confused, could you please elaborate on the properties that you mentioned before.
thanks

Mark44
Mentor
10a2 - 3b2 is not the right answer. What does a2 even mean?

What's a $\cdot$ (b + c)?
What's a $\cdot$ a?

ok, so using the distributive property of Dot product, I got:

-10a2+2 ab + 15 ab - 3b2

Simplifying we get:

-10a2+ 17 ab - 3b2

is this correct?

Mark44
Mentor
No, this is incorrect for two reasons.
a$\cdot$a $\neq$a2. These are vectors and they are being multiplied using the dot product. There is a property of the dot product that allows you to do something with a$\cdot$a.

Also, two of your three coefficients are wrong.

No, this is incorrect for two reasons.
a$\cdot$a $\neq$a2. These are vectors and they are being multiplied using the dot product. There is a property of the dot product that allows you to do something with a$\cdot$a.

Also, two of your three coefficients are wrong.
I always thought that
a.a = lal2 (this isn't correct?)

Two of my three coefficients are wrong? (please note that I made a mistake copying down the question in my first post, it is actually -2 a instead of 2 a). Is this correct?

Thanks..

Mark44
Mentor
I always thought that
a.a = lal2 (this isn't correct?)
This is correct.
Two of my three coefficients are wrong? (please note that I made a mistake copying down the question in my first post, it is actually -2 a instead of 2 a). Is this correct?

Thanks..
OK, then the coefficients are correct, but you shouldn't write a2, b2, or ab. All of these are dot products, and you should simplify the a.a and b.b terms.