Let A, B, C be three points whose position vectors respectively are a = i + 4 j + 3 k b = 2 i + α j + 4 k, α R c = 3 i - 2 j + 5 k If α is the smallest positive integer for which a, b, c are noncollinear, then the length of the median, in Δ ABC, through A is:

Vector Algebra: JEE Main 2022 Mathematics question

JEE Main 2022 · 29 Jun, Evening shift · Q5695

JEE Main 202229 Jun, Evening shiftMathematicsMediumVector Algebra184× since 2002

Let A, B, C be three points whose position vectors respectively are

\overrightarrow a = \widehat i + 4\widehat j + 3\widehat k

\overrightarrow b = 2\widehat i + \alpha \widehat j + 4\widehat k,\,\alpha \in R

\overrightarrow c = 3\widehat i - 2\widehat j + 5\widehat k

\alpha

is the smallest positive integer for which

\overrightarrow a ,\,\overrightarrow b ,\,\overrightarrow c

are noncollinear, then the length of the median, in

\Delta

ABC, through A is :