Match List-I with List-II
| List-I | List-II | ||
| (A) | The distance of a point \( P(a,b,c) \) from x-axis | (I) | \( \sqrt{a^2+b^2+c^2} \) |
| (B) | The distance of a point \( P(a,b,c) \) from y-axis | (II) | \( \sqrt{b^2+c^2} \) |
| (C) | The distance of a point \( P(a,b,c) \) from Z-axis | (III) | \( \sqrt{a^2+c^2} \) |
| (D) | The distance of a point \( P(a,b,c) \) from origin | (IV) | \( \sqrt{a^2+b^2} \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) - (II), (B) - (III), (C) - (IV), (D) - (I)
The foot of the perpendicular from P(a, b, c) to an axis keeps the coordinate along that axis and makes the other two zero. The distance is then found with the distance formula.
(A) Distance from the x-axis
This matches (II) \( \sqrt{b^2+c^2} \). The foot is (a, 0, 0):
\( \displaystyle \sqrt{(a-a)^2+(b-0)^2+(c-0)^2}=\sqrt{b^2+c^2} \)
(B) Distance from the y-axis
This matches (III) \( \sqrt{a^2+c^2} \). The foot is (0, b, 0):
\( \displaystyle \sqrt{a^2+0+c^2}=\sqrt{a^2+c^2} \)
(C) Distance from the z-axis
This matches (IV) \( \sqrt{a^2+b^2} \). The foot is (0, 0, c):
\( \displaystyle \sqrt{a^2+b^2+0}=\sqrt{a^2+b^2} \)
(D) Distance from the origin
This matches (I) \( \sqrt{a^2+b^2+c^2} \), by the distance formula from (0, 0, 0).
So the matching is (A) - (II), (B) - (III), (C) - (IV), (D) - (I).