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Moderate

Vector Algebra Rules With Dot Product

LINALG-XK4CGG

Let $\vec u,\vec v,\vec w$ be vectors in $\mathbb{R}^n$ and $a,b$ be real numbers.

Which of the following equations is true for all choices of $\vec u,\vec v,\vec w,a,b$?

Select ALL that apply.

A

$(a\vec v)\cdot(a\vec w)=a(\vec v\cdot \vec w)$

B

$(ab)\vec v=a(b\vec v)$

C

$\vec v\cdot \vec w=\vec w\cdot \vec v$

D

$a(\vec v\cdot \vec w)=(a\vec v)\cdot \vec w$

E

$(\vec u+\vec v)\cdot \vec w=\vec u+(\vec v\cdot \vec w)$