If a² + b² + c² = 16, x² + y² + z² = 25 and ax + by + cz = 20 then the value of $$\frac{{a + b + c}}{{x + y + z}}$$   = ?

Solution(By Examveda Team)

$$\eqalign{ & {a^2} + {b^2} + {c^2} = 16,{\text{ }}{x^2} + {y^2} + {z^2} = 25{\text{ }} \cr & {\text{But }}b = c = 0,{\text{ But }}y = z = 0 \cr & {\text{}}a = 4{\text{ }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x = 5 \cr & {\text{Now, }} \cr & ax + by + cz = 20 \cr & 4 \times 5 + 0 + 0 = 20 \cr & 20 = 20{\text{ }}\left( {{\text{Satisfy}}} \right) \cr & {\text{Now, }}\frac{{a + b + c}}{{x + y + z}} \cr & = \frac{{4 + 0 + 0}}{{5 + 0 + 0}} \cr & = \frac{4}{5} \cr} $$