JEE 2023 Mathematics PYQ — Let a line pass through the point and be parallel to the line . I… | Mathem Solvex | Mathem Solvex
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JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023
Let a line L pass through the point P(2,3,1) and be parallel to the line x+3y−2z−2=0=x−y+2z. If the distance of L from the point (5,3,8) is α, then 3α2 is equal to ________.
Choose the correct answer:
A.
158
(Correct Answer)
B.
159
C.
160
D.
161
Correct Answer:
158
Explanation
Solution
Step 1: Find the direction vector of the line L
The line L is parallel to the intersection of two planes:
P1:x+3y−2z−2=0 (Normal vector n1=i^+3j^−2k^)
P2:x−y+2z=0 (Normal vector n2=i^−j^+2k^)
The direction vector v of line L is given by the cross product of the normals:
