Say we have an orthonormal basis in RR^3 {A,B,C}. Then when taking the cross product of any 2 of these, we know it is equal to either the third basis element, or −1 times that element. Say we are given A xx B=C, and we want to know whether A xx C=B or A xx C=−B. Via the right-hand rule, I can see that it should be −B, but how can I show this algebraically, using only what is given here?

Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to the given matrix
$$\left[\begin{array}{cccc}1& 3& 0& -4\\ 2& 6& 0& -8\end{array}\right]$$

Find, correct to the nearest degree, the three angles of the triangle with the given vertices
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Whether f is a function from Z to R if 
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b) ${\displaystyle f\left(n\right)=\sqrt{n^2+1}}$. 
c) ${\displaystyle f\left(n\right)=\frac{1}{n^2-4}}$.

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The solution set of $\tan <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}=3\cot <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}$ is

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