Verify the Distributive Law?

[whig4life]

Not sure what this question is asking me to do multivariable Calculus-wise? e.g. what am I supposed to learn/demonstrate from this? Any/all help would be appreciated.

 

[Deleted member 4993]

Not sure what this question is asking me to do multivariable Calculus-wise? e.g. what am I supposed to learn/demonstrate from this? Any/all help would be appreciated.

First calculate v + w and let that be = q

Then calculate u . q = p

Then calculate u . v = m

And u. w = n

Finally show p = m + n

 

[HallsofIvy]

The "distributive law", in any algebraic system in which we have definitions of "addition" and "multiplication", says that a(b+ c)= ab+ ac. That's probably shown on page 676. And I would suggest that what they "asking you to do" is exactly what they said:

Let \(\displaystyle \vec{u}= <a_1, b_1, c_1>\), [itex]\vec{v}= <a_2, b_2, c_2>[/tex], and \(\displaystyle \vec{w}= <a_3, b_3, c_3>\).

Now, in terms of those, what is \(\displaystyle \vec{v}+ \vec{w}\)? What is \(\displaystyle \vec{u}\cdot)(\vec{v}+ \vec{w})\)?

What is \(\displaystyle \vec{u}\cdot\vec{v}\)? What is \(\displaystyle \vec{u}\cdot\vec{w}\)?

What is \(\displaystyle \vec{u}\cdot\vec{v}+ \vec{u}\cdot\vec{w}\)?