Consider the matrix $$A = \begin{pmatrix}3 & 5 & 11 \\5 & 9 & 20\\11&20&49\end{pmatrix}$$
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Could someone please solve the first question, that is the magnitude of $v_2$ . I am not sure which column the vectors belong to, thus I am unable to solve any of the parts. $$\begin{pmatrix}v_1v_1 &v_1v_2 & v_1v_3\\ v_2v_1 &v_2v_2& v_2v_3\\ v_3v_1 &v_3v_2 &v_3v_3\end{pmatrix}$$
The problem says that the entries of the matrix are given by the dot product of the vectors in $\mathbb R^4$.
For instance, $$ 3 = a_{11} = \vec v_1 \cdot \vec v_1 \\5 = a_{12} = \vec v_1 \cdot \vec v_2\\11 = a_{13} = \vec v_1 \cdot \vec v_3$$ and so on.
Here, the matrix $A$ has the form $$A = \begin{pmatrix}a_{11} & a_{12} & a_{13}\\a_{21} & a_{22} & a_{23}\\a_{31} & a_{32} & a_{33}\end{pmatrix}$$
Extra: Here are some useful hints:
i) $\|\vec v_2\|^2 = \vec v_2 \cdot \vec v_2$;
ii) $\|\vec v_1 + \vec v_2\| \leq \|\vec v_1\| + \|\vec v_2\|$;
iii) $\cos \theta = \frac{\langle \vec v_2, \vec v_3\rangle}{\|\vec v _2\| \|\vec v_3\|}$, where $\theta$ is the angle between $\vec v_2$ and $\vec v_3$.
Just a few ideas so you can get started.