Question : If $a^{2} + b^{2} + c^{2} = 16$ , $x^{2} + y^{2} + z^{2} = 25$ and $a x + b y + c z = 20$ , then the value of $\frac{a + b + c}{x + y + z}$ is:
Option 1: $\frac{3}{5}$
Option 2: $\frac{5}{3}$
Option 3: $\frac{4}{5}$
Option 4: $\frac{5}{4}$

Question

Question : If $a^{2} = b y + c z$ , $b^{2} = c z + a x$ , $c^{2} = a x + b y$ , then the value of $\frac{x}{a + x} + \frac{y}{b + y} + \frac{z}{c + z}$ is:

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Answer 1

Correct Answer: $\frac{4}{5}$

Solution : Given: $a^{2} + b^{2} + c^{2} = 16$ ----(equation 1)
$x^{2} + y^{2} + z^{2} = 25$ -----(equation 2)
$a x + b y + c z = 20$ -----(equation 3)
Substitute the values of $b = 0$ and $c = 0$ in the given equation 1, we get,
$a^{2} + 0^{2} + 0^{2} = 16$
$\Rightarrow a^{2} = 16$
$∴ a = 4$
Substitute the values of $y = 0$ and $z = 0$ in the given equation 2, we get,
$x^{2} + 0^{2} + 0^{2} = 25$
$\Rightarrow x^{2} = 25$
$∴ x = 5$
Substitute the values in the given equation 3, we get,
$4 \times 5 + 0 \times 0 + 0 \times 0 = 20$
$\Rightarrow 20 = 20$
So, the above equation is satisfied.
Substitute the values in the given below equation, we get,
$∴ \frac{a + b + c}{x + y + z} = \frac{4 + 0 + 0}{5 + 0 + 0} = \frac{4}{5}$
Hence, the correct answer is $\frac{4}{5}$ .

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Question : If a2+b2+c2=16, x2+y2+z2=25 and ax+by+cz=20, then the value of a+b+cx+y+z is:Option 1: 35Option 2: 53Option 3: 45Option 4: 54

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Question : If $a^{2} + b^{2} + c^{2} = 16$ , $x^{2} + y^{2} + z^{2} = 25$ and $a x + b y + c z = 20$ , then the value of $\frac{a + b + c}{x + y + z}$ is:
Option 1: $\frac{3}{5}$
Option 2: $\frac{5}{3}$
Option 3: $\frac{4}{5}$
Option 4: $\frac{5}{4}$