Match List-I with List-II
|
List-I Lines |
List-II Direction Ratios |
|
(A) $\frac{x-1}{2} = \frac{2-y}{1}=z$ |
(I) 1, 3, -1 |
|
(B) $\frac{2x-1}{2}=\frac{y+1}{3}=\frac{1-z}{1}$ |
(II) 2, -2, 0 |
|
(C) $\frac{x+1}{2}=\frac{3-y}{2},z=2$ |
(III) 2, -1, 1 |
|
(D) $\frac{2x-3}{4}=\frac{1-2y}{2}=\frac{z}{5}$ |
(IV) 2, -1, 5 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(III), (B)-(I), (C)-(II), (D)-(IV)
|
List-I Lines |
List-II Direction Ratios |
|
(A) $\frac{x-1}{2} = \frac{2-y}{1}=z$ |
(III) 2, -1, 1 |
|
(B) $\frac{2x-1}{2}=\frac{y+1}{3}=\frac{1-z}{1}$ |
(I) 1, 3, -1 |
|
(C) $\frac{x+1}{2}=\frac{3-y}{2},z=2$ |
(II) 2, -2, 0 |
|
(D) $\frac{2x-3}{4}=\frac{1-2y}{2}=\frac{z}{5}$ |
(IV) 2, -1, 5 |
Extract direction ratios from each line.
(A) $\displaystyle \frac{x-1}{2}=\frac{2-y}{1}=z=t$
$x=1+2t,\; y=2-t,\; z=t$
Direction ratios: $(2,-1,1)$ → matches (III)
(B) $\displaystyle \frac{2x-1}{2}=\frac{y+1}{3}=\frac{1-z}{1}=t$
$x=\frac{1+2t}{2},\; y=-1+3t,\; z=1-t$
Direction ratios: $(1,3,-1)$ → matches (I)
(C) $\displaystyle \frac{x+1}{2}=\frac{3-y}{2}=t,\; z=2$
$x=-1+2t,\; y=3-2t,\; z$ constant
Direction ratios: $(2,-2,0)$ → matches (II)
(D) $\displaystyle \frac{2x-3}{4}=\frac{1-2y}{2}=\frac{z}{5}=t$
$x=\frac{3+4t}{2},\; y=\frac{1-2t}{2},\; z=5t$
Direction ratios: $(2,-1,5)$ → matches (IV)
Final matching:
(A)–(III), (B)–(I), (C)–(II), (D)–(IV)