a+b+cx+y+za+b+cx+y+z\frac{{a + b + c}}{{x + y + z}} = ?" /> a+b+cx+y+za+b+cx+y+z\frac{{a + b + c}}{{x + y + z}} = ?" /> a+b+cx+y+za+b+cx+y+z\frac{{a + b + c}}{{x + y + z}} = ?" />

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

1 $\frac{3}{5}$ $\frac{3}{5}$
2 $\frac{4}{5}$ $\frac{4}{5}$
3 $\frac{5}{3}$ $\frac{5}{3}$
4 $\frac{5}{4}$ $\frac{5}{4}$

Answer:- 1

Explanation:-

Solution:

\begin{aligned} a^{2} + b^{2} + c^{2} = 16, x^{2} + y^{2} + z^{2} = 25 \\ But b = c = 0, But y = z = 0 \\ a = 4 x = 5 \\ Now, a x + b y + c z = 20 \\ 4 \times 5 + 0 + 0 = 0 \\ 20 = 20 (Satisfy) \\ Now, \frac{a + b + c}{x + y + z} \\ = \frac{4 + 0 + 0}{5 + 0 + 0} \\ = \frac{4}{5} \end{aligned}

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

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= ?", "text": "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}

$\frac{{a + b + c}}{{x + y + z}}$ = ?", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} a^{2} + b^{2} + c^{2} = 16, x^{2} + y^{2} + z^{2} = 25 \\ But b = c = 0, But y = z = 0 \\ a = 4 x = 5 \\ Now, a x + b y + c z = 20 \\ 4 \times 5 + 0 + 0 = 0 \\ 20 = 20 (Satisfy) \\ Now, \frac{a + b + c}{x + y + z} \\ = \frac{4 + 0 + 0}{5 + 0 + 0} \\ = \frac{4}{5} \end{aligned}

$\eqalign{ & {a^2} + {b^2} + {c^2} = 16,{\text{ }}{x^2} + {y^2} + {z^2} = 25{\text{ }} \cr & {\text{But }}b = c = 0,{\text{ But }}y = z = 0 \cr & {\text{ }}a = 4{\text{ }}x = 5 \cr & {\text{Now, }}ax + by + cz = 20 \cr & 4 \times 5 + 0 + 0 = 0 \cr & 20 = 20{\text{ }}\left( {{\text{Satisfy}}} \right) \cr & {\text{Now, }}\frac{{a + b + c}}{{x + y + z}} \cr & = \frac{{4 + 0 + 0}}{{5 + 0 + 0}} \cr & = \frac{4}{5} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} a^{2} + b^{2} + c^{2} = 16, x^{2} + y^{2} + z^{2} = 25 \\ But b = c = 0, But y = z = 0 \\ a = 4 x = 5 \\ Now, a x + b y + c z = 20 \\ 4 \times 5 + 0 + 0 = 0 \\ 20 = 20 (Satisfy) \\ Now, \frac{a + b + c}{x + y + z} \\ = \frac{4 + 0 + 0}{5 + 0 + 0} \\ = \frac{4}{5} \end{aligned}

$\eqalign{ & {a^2} + {b^2} + {c^2} = 16,{\text{ }}{x^2} + {y^2} + {z^2} = 25{\text{ }} \cr & {\text{But }}b = c = 0,{\text{ But }}y = z = 0 \cr & {\text{ }}a = 4{\text{ }}x = 5 \cr & {\text{Now, }}ax + by + cz = 20 \cr & 4 \times 5 + 0 + 0 = 0 \cr & 20 = 20{\text{ }}\left( {{\text{Satisfy}}} \right) \cr & {\text{Now, }}\frac{{a + b + c}}{{x + y + z}} \cr & = \frac{{4 + 0 + 0}}{{5 + 0 + 0}} \cr & = \frac{4}{5} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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