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Question

Mathematics Question on Three Dimensional Geometry

Let y ∈ R be such that the lines L1:x+111=y+212=z+293L_1:\frac{x+11}{1}=\frac{y+21}{2}=\frac{z+29}{3} and L2:x+163=y+112=z+4γL_2:\frac{x+16}{3}=\frac{y+11}{2}=\frac{z+4}{\gamma} intersect. Let R1 be the point of intersection of L1 and L2. Let O = (0, 0 ,0), and n^\hat{n} denote a unit normal vector to the plane containing both the lines L1 and L2.

Match each entry in List-I to the correct entry in List-II.List - IList - II
(P)γ equals
(Q)A possible choice for n^\hat{n} is
(R)OR1\overrightarrow{OR_1} equals
(S)A possible value of OR1.n^\overrightarrow{OR_1}.\hat{n} is
(5)
The correct option is
A

(P) → (3) (Q) → (4) (R) → (1) (S) → (2)

B

(P) → (5) (Q) → (4) (R) → (1) (S) → (2)

C

(P) → (3) (Q) → (4) (R) → (1) (S) → (5)

D

(P) → (3) (Q) → (1) (R) → (4) (S) → (5)

Answer

(P) → (3) (Q) → (4) (R) → (1) (S) → (5)

Explanation

Solution

The correct option is (C):(P) → (3) (Q) → (4) (R) → (1) (S) → (5).