I have the points O,A,B and C. Relative to O, the position vectors of A, B and C are (1,4,2), (3,3,3), (2,−1,1) Want to show that the lines OB and AC bisect each other. Is it sufficient to show that 1/2 vec(OB)=vec(OA)+1/2 vec(AC)? Are there other ways using vectors?

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

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Whether f is a function from Z to R if 
a) ${\displaystyle f\left(n\right)=\pm n}$. 
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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