What is the length of foot of perpendicular drawn from the point P (3, 4, 5) on y-axis
(A) √41
(B) √34
(C) 5
(D) none of these
(B) √34
Explanation:
As we know that y-axis lies on x y plane and y z.
So, its distance from x y and y z plane is 0.
∴ By basic definition of three-dimension coordinate we can say that x-coordinate and z–coordinate are 0.
As, perpendicular is drawn from point P to y-axis, so distance of point of intersection of this line from x z plane remains the same.
∴ y-coordinate of the new point say Q = 4
Or we can say that corresponding point on y-axis is (0, 4, 0)
∴ Length of perpendicular = distance between P and Q
$\sqrt{(3-0)^{2}+(4-4)^{2}+(5-0)^{2}}=\sqrt{9+25}=\sqrt{34}$. From distance formula-
PQ =
∴ Length of foot of perpendicular drawn from the point P (3, 4, 5) on y-axis is √34 units.
Hence, option (B) is the only correct choice.