Question

Perpendiculars AP, AQ and AR are drawn to the $x-,y-$ and $z-$axes, respectively, from the point $A(1,-1,2)$. The A.M. of $A{P}^2,$ $A{Q}^2$ and $A{R}^2$ is

• A. $4$
• B. $5$
• C. $3$
• D. $2$

Answer 1

The correct option is A $4$

$A=(1,-1,2),P=(1,0,0),,Q=(0,-1,0),R=(0,0,2)$

$A{P}^2=\left[\right(-1{)}^2+2^2]=5$,

$A{Q}^2=[1^2+2^2]=5$,

$A{R}^2=\left[\right(-1{)}^2+1^2]=2$

Hence required A.M is $=\frac{5+5+2}{3}=4$