JEE 2022 Mathematics PYQ — Let be three points whose position vectors respectively are If is… | Mathem Solvex | Mathem Solvex
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JEE 2022 — Mathematics PYQ
JEE | Mathematics | 2022
Let A,B,C be three points whose position vectors respectively are
a=i^+4j^+3k^
b=2i^+αj^+4k^,α∈R
c=3i^−2j^+5k^If α
is the smallest positive integer for which a,b,c are noncollinear, then the length of the median, in ΔABC, through A is:
Choose the correct answer:
A.
282
(Correct Answer)
B.
262
C.
269
D.
266
Correct Answer:
282
Explanation
Solution
1. Find α for collinearity
If A,B,C are collinear, AB is parallel to AC.
AB=(2−1)i^+(α−4)j^+(4−3)k^=i^+(α−4)j^+k^
AC=(3−1)i^+(−2−4)j^+(5−3)k^=2i^−6j^+2k^
For collinearity: 21=−6α−4=21.
−3=α−4⟹α=1.
The problem states α is the smallest positive integer for which they are noncollinear. Since α=1 makes them collinear, the next smallest positive integer is α=2.
The problem states α is the smallest positive integer for which they are noncollinear. Since α=1 makes them collinear, the next smallest positive integer is α=2.
