MCQMediumJEE Main 2023 · 24 January, Shift 2Dot Product

Mathematics Question from JEE Main 2023 · 24 January, Shift 2

Let α⃗=4i^+3j^+5k^\vec{\alpha} = 4\hat{i} + 3\hat{j} + 5\hat{k} and β⃗=i^+2j^−4k^\vec{\beta} = \hat{i} + 2\hat{j} - 4\hat{k}. Let β⃗1\vec{\beta}_1 be parallel to α⃗\vec{\alpha} and β⃗2\vec{\beta}_2 be perpendicular to α⃗\vec{\alpha}. If β⃗=β⃗1+β⃗2\vec{\beta} = \vec{\beta}_1 + \vec{\beta}_2, then the value of 5β⃗2⋅(i^+j^+k^)5\vec{\beta}_2 \cdot (\hat{i} + \hat{j} + \hat{k}) is:

  • A

    66

  • B

    1111

  • C

    77

  • D

    99

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