Verified Solution • 2025–26 Session moderate

QJEEM22Mab9bd: JEE Main 2022 Physics - Class 11 JEEM22Mab9bd Solution: Let A, B, C be three points whose position vectors respectively …

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 :

Multiple Choice Options

  • A 822
  • B 622
  • C 692
  • D 662

Step-by-Step Verified Solution

AB→∥AC→\overrightarrow{A B} \| \overrightarrow{A C} if

12=α−4−6=12\frac{1}{2}=\frac{\alpha-4}{-6}=\frac{1}{2}

⇒α=1\Rightarrow \alpha=1

a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c} are non-collinear for α=2\alpha=2 (smallest positive integer)

Mid point of BC=M(52,0,92)B C=M\left(\frac{5}{2}, 0, \frac{9}{2}\right)

AM=94+16+94=822A M=\sqrt{\frac{9}{4}+16+\frac{9}{4}}=\frac{\sqrt{82}}{2}

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