Mathematics: If r = x, y, z and r0 = x0, y0, z0 , describe the set of all points (x, y, z) such that |r − r0| = 5.

She can do 12 combinations. IT is 2 for every 1 book. 2*6 is 12. If you posted this here and you are in high school you might be overthinking it...

If r = x, y, z and r0 = x0, y0, z0 , describe

Ответ:

sashajayne8260

02.01.2022

Mathematics

Point $\left ( x,y,z\right )$ represents a sphere

Step-by-step explanation:

Take $r=\left ( x,y,z \right )\,,\,r_0=\left ( x_0,y_0,z_0 \right )$

We need to describe the set of all points (x, y, z) such that $\left | r-r_0 \right |=5$

Solution :

For $r-r_0=\left ( x,y,z \right )-\left ( x_0,y_0,z_0 \right )$ , we will subtract the respective elements .

$r-r_0=\left ( x,y,z \right )-\left ( x_0,y_0,z_0 \right )=\left ( x-x_0,y-y_0,z-z_0 \right )$

Therefore, $\left | r-r_0 \right |=\sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2}$

As $\left | r-r_0 \right |=5$ , we get

$\sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2}=5$

On squaring both sides, we get

$\left ( \sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2} \right )^2=5^2\\(x-x_0)^2+(y-y_0)^2+(z-z_0)^2=25$

The general equation of a sphere is (x - a)² + (y - b)² + (z - c)² = r², where (a, b, c) denotes the center of the sphere and r represents the radius .

So, (x-x_0)^2+(y-y_0)^2+(z-z_0)^2=25 represents a sphere with center as $\left ( x_0,y_0,z_0 \right )$ and radius equal to 5 units

0,0(0 оценок)

If r = x, y, z and r0 = x0, y0, z0 , describe the set of all points (x, y, z) such that |r − r0| = 5.

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question