Question

Find the point on z axis which are at a distance root 21 from the point 1.2.3

Answer 1

Above file contains your answer. Hope it will help you.

Answer 2

The point on z- axis is (0,0,-1) and (0,0,7)

Step-by-step explanation:

1. Let point on z-axis is A.Coordinate of point A is

  $\mathbf{(x_{1},y_{1}.z_{1})=(0,0,a)}$     ...1)

2. Given another point let it is point B, which coordinate are

  $\mathbf{(x_{2},y_{2}.z_{2})=(1,2,3)}$     ...2)

3. We know distance formula between two point are

  $\mathbf{D=\sqrt{\left [ (x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}+(z_{1}-z_{2})^{2} \right ]}}$        ...3)

4. Where distance between point A and B is $\mathbf{\sqrt{21}}$.

 

 From equation 3)

 $\mathbf{\sqrt{\left [ (x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}+(z_{1}-z_{2})^{2} \right ]}=D}$

 So

 $\mathbf{\sqrt{\left [ (0-1)^{2}+(0-2)^{2}+(a-3)^{2} \right ]}=\sqrt{21}}$

 Which can be written as

 $\mathbf{(0-1)^{2}+(0-2)^{2}+(a-3)^{2}=21}$         ...4)

5. On solving equation 4), we get

    $\mathbf{(a-3)^{2}=16}$        

   It will become on solving above equation

   a-3 = +4        ...5)

   and

   a-3 = -4         ...6)

6. On solving equation 5) and equation 6), we get

   a= +7   and a= -1               ...7)

7. Coordinate of point A on z- axis is (0,0,-1) and (0,0,7)