Question

If L, M are the feet of the perpendiculars from $(2,4,5)$ to the xy-plane, yz-plane respectively ,then the distance LM is

Answer 1

Let the given point be A($2,4,5$)

Taking projection of point A on X-Y plane we get point ($2,4,0$)

so, point L is ($2,4,0$)

again taking projection of point A on X-Y plane we get point ($0,4,5$)

so,point M is ($0,4,5$)

Therefore, LM= $\sqrt{{(0-2)}^2+{(4-4)}^2+{(5-0)}^2}$

=$\sqrt{4+25}$

=$\sqrt{29}$