JEE 2022 Mathematics PYQ — Let be a plane. Let be another plane which passes through the poi… | Mathem Solvex | Mathem Solvex
Tip:A–D to answerE for explanationV for videoS to reveal answer
JEE 2022 — Mathematics PYQ
JEE | Mathematics | 2022
Let P1:r⋅(2i^+j^−3k^)=4 be a plane. Let P2 be another plane which passes through the points (2,−3,2),(2,−2,−3) and (1,−4,2). If the direction ratios of the line of intersection of P1 and P2 be 16,α,β, then the value of α+β is equal to:
Choose the correct answer:
A.
28
(Correct Answer)
B.
29
C.
30
D.
31
Correct Answer:
28
Explanation
Solution
The normal vector of P1 is n1=(2,1,−3).
For P2, vectors in the plane are v1=(0,1,−5) and v2=(−1,−1,0).
The normal to P2 is n2=v1×v2=(−5,5,1).
The direction of the line of intersection is d=n1×n2=(16,13,15).
Comparing with (16,α,β), we get α=13 and β=15.
Final Value:α+β=28.
Explanation
Solution
The normal vector of P1 is n1=(2,1,−3).
For P2, vectors in the plane are v1=(0,1,−5) and v2=(−1,−1,0).
The normal to P2 is n2=v1×v2=(−5,5,1).
The direction of the line of intersection is d=n1×n2=(16,13,15).
