Question

If $A,B$ are the feet of the perpendiculars from $(2,4,5)$ to the $x$-axis, $y$-axis respectively, then the distance $AB$ is

• A. $2\sqrt{5}$
• B. $\sqrt{29}$
• C. $\sqrt{41}$
• D. $3\sqrt{5}$

Answer 1

Answer: (A)

$2\sqrt{5}$

Since the point is given by $(2,4,5)$ and $A,B$ are the projections on the $x$ and $y$ axes respectively,
$A=(2,0,0),B=(0,4,0)$
The distance $AB$ is given by $\sqrt{(2^2+4^2)}=\sqrt{20}=2\sqrt{5}$