Let α = 4i + 3j + 5k and β = i + 2j - 4k. Let β₁ be parallel to α… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 24 January, Shift 2Dot Product

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

A
$6$
B
$11$
C
$7$
D
$9$

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