Match the following pairs of lines. Match the following. List-I List-II (A) 2 x − 1 = 3 y − 2 = 4 z − 3 and 3 x − 1 = 4 y − 3 = 5 z − 5 are. (p) Coincident (B) 2 x − 1 = 3 y − 2 = 4 z

Question

Match the following pairs of lines.

Match the following.

List-I	List-II
(A) $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ and $\frac{x - 1}{3} = \frac{y - 3}{4} = \frac{z - 5}{5}$ are.	(p) Coincident
(B) $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ and $\frac{x - 3}{2} = \frac{y - 5}{3} = \frac{z - 7}{4}$ are.	(q) Parallel and different
(C) $\frac{x - 2}{5} = \frac{y + 3}{4} = \frac{5 - z}{2}$ and $\frac{x - 7}{5} = \frac{y - 1}{4} = \frac{z - 2}{- 2}$ are.	(r) Skew
(D) $\frac{x - 3}{2} = \frac{y + 2}{3} = \frac{z - 7}{5}$ and $\frac{x - 3}{3} = \frac{y - 2}{2} = \frac{z - 7}{5}$ are.	(s) Intersecting in a point
	(t) coplanar

TestHub · Accepted Answer

(A) Both the lines pass through the point (7, 11, 15): intersecting, hence coplanar → s, t. (B) <2, 3, 4> are direction ratios of both the lines and the point (1, 2, 3) is common to both: the lines are coincident → p, t. (C) Direction ratios ⟨ 5 , 4 , − 2 ⟩ for both; substituting the parametric forms gives no value of λ : the lines are parallel and different → q. (D) Direction ratios ⟨ 2 , 3 , 5 ⟩ and ⟨ 3 , 2 , 5 ⟩ : not parallel. Solving 3 + 2 λ = 3 + 3 μ and − 2 + 3 λ = 2 + 2 μ gives λ = 5 12 ​ , μ = 5 8 ​ , but then z = 7 + 5 λ = 19  = 7 + 5 μ = 15 : the lines do not intersect, hence skew → r.

Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

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