Question

The distances of the point $P(1,2,3)$ from the coordinates axes are:

• A. $\sqrt{13},\sqrt{10},\sqrt{5}$
• B. $\sqrt{11},\sqrt{10},\sqrt{5}$
• C. $\sqrt{13},\sqrt{20},\sqrt{15}$
• D. $\sqrt{23},\sqrt{10},\sqrt{5}$

Answer 1

The correct option is A $\sqrt{13},\sqrt{10},\sqrt{5}$

The point: $(1,2,3)$

$\therefore$ Co-ordinates axes are $(1,0,0),(0,2,0),(0,0,3)$

Distance of $(1,2,3)$ from $(1,0,0)$

$=\sqrt{(1-1{)}^2+(0-2{)}^2+(0-3{)}^2)}$

$=\sqrt{4+9}=\sqrt{13}$

Distance of $(1,2,3)$ from $(0,2,0)$

$=\sqrt{(0-1{)}^2+(2-2{)}^2+(0-3{)}^2)}$

$=\sqrt{1+9}=\sqrt{10}$

Distance of $(1,2,3)$ from $(0,0,3)$

$=\sqrt{(0-1{)}^2+(0-2{)}^2+(3-3{)}^2)}$

$=\sqrt{5}$

Hence, the distances of the point $P(1,2,3)$ from the coordinates axes$=\sqrt{13},\sqrt{10},\sqrt{5}$