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Vector Algebra question

2022 · 29 Jun · Shift 2 · Q32
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  5. /2022 · 29 Jun · Shift 2 · Q32

Vector Algebra question

2022 · 29 Jun · Shift 2 · Q32

JEE MainMathematicsVector AlgebraMCQ+4 / −1
Let A, B, C be three points whose position vectors respectively are a→=i^+4j^+3k^b→=2i^+αj^+4k^, α∈Rc→=3i^−2j^+5k^\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 ka=i+4j​+3kb=2i+αj​+4k,α∈Rc=3i−2j​+5k If α\alphaα is the smallest positive integer for which a→, b→, c→\overrightarrow a ,\,\overrightarrow b ,\,\overrightarrow ca,b,c are noncollinear, then the length of the median, in Δ\DeltaΔ ABC, through A is :
  1. A
    822{{\sqrt {82} } \over 2}282​​
  2. B
    622{{\sqrt {62} } \over 2}262​​
  3. C
    692{{\sqrt {69} } \over 2}269​​
  4. D
    662{{\sqrt {66} } \over 2}266​​
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