1. Yes, the three vectors are mutually orthogonal.

2. Yes, the three vectors are mutually orthogonal.

3. Yes, the three vectors are mutually orthogonal.

4. Yes, the three vectors are mutually orthogonal.

5. $a^2=7\text{,}{b}^2=7\text{,}{c}^2=14$

6. $a^2=18\text{,}{b}^2=18\text{,}{c}^2=36$

7. $a^2=19\text{,}{b}^2=25\text{,}{c}^2=44$

8. $a^2=103\text{,}{b}^2=112\text{,}{c}^2=215$

9. $\angle A=\angle B=45°$

10. $\angle A=\angle B=45°$

11. $\angle A=41.08°\text{,}\angle B=48.92°$

12. $\angle A=43.80°\text{,}\angle B=46.20°$

13. ${\mathbf{u}}_1=(2,1,0)\text{,}{\mathbf{u}}_2=(-3,0,1)$

14. ${\mathbf{u}}_1=(-5,1,0)\text{,}{\mathbf{u}}_2=(3,0,1)$

15. ${\mathbf{u}}_1=(2,1,0,0)\text{,}{\mathbf{u}}_2=(3,0,1,0)\text{,}{\mathbf{u}}_3=(-5,0,0,1)$

16. ${\mathbf{u}}_1=(-7,1,0,0)\text{,}{\mathbf{u}}_2=(6,0,1,0)\text{,}{\mathbf{u}}_3=(9,0,0,1)$

17. ${\mathbf{u}}_1=(7,-3,1,0)\text{,}{\mathbf{u}}_2=(-19,5,0,1)$

18. ${\mathbf{u}}_1=(-12,-3,1,0)\text{,}{\mathbf{u}}_2=(16,7,0,1)$

19. ${\mathbf{u}}_1=(-13,4,1,0,0)\text{,}{\mathbf{u}}_2=(4,-3,0,1,0)\text{,}{\mathbf{u}}_3=(-11,4,0,0,1)$

20. ${\mathbf{u}}_1=(-5,1,1,0,0)\text{,}{\mathbf{u}}_2=(-12,4,0,1,0)\text{,}{\mathbf{u}}_3=(-19,7,0,0,1)$

21. ${\mathbf{u}}_1=(-1,-1,1,0,0)\text{,}{\mathbf{u}}_2=(0,-1,0,-1,1)$

22. ${\mathbf{u}}_1=(-2,1,1,0,0)\text{,}{\mathbf{u}}_2=(1,-2,0,1,0)$