Question

Find the point on Z-axis which are at a distance $\sqrt{21}$ unit from the point$(1,2,3)$

Answer 1

Let the point on Z axis be given as $(0,0,z)$. The distance between $(1,2,3)$ and $(0,0,z)$ is given as $\sqrt{1^2+2^2+(3-z{)}^2}=\sqrt{21}$

$5+(3-z{)}^2=21$

$z^2-6z-7=0$

$z=7,z=-1$

Hence points are $(0,0,7),(0,0,-1)$