- There is an infinity of orthogonal matrices $Q=[q_1,q_2,q_3]$ that have as the first two columns the vectors $q_1=\frac{1}{\sqrt{6}}(-1,2,-1)^T,q_2=\frac{1}{\sqrt{3}}(1,1,1)^T$.
I would say this is not true since there is only one third vector orthogonal on other two. - If $\langle u,v\rangle \ge 0$ then the measure of the angle between $u$ and $v$ is less than $\frac{\pi}{2}$
To me it looks true, since the measure can take values only in interval (0,1) - The projection of a line on a plane is always a line.
True?
Thank you for taking your time.