What is the length of foot of perpendicular

Question:

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

Solution:

(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.

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