In this case, the correct dot product is 22a.a + 15a.b - 3b.b.

[spoc21]

Homework Statement

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

Homework Equations

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..

 

[Mark44]

Homework Statement

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

Homework Equations

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.

 

[spoc21]

like 10 a ² - 3 b²

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

 

[Mark44]

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

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

 

[spoc21]

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]

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.

 

[spoc21]

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]

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.