Let a = i + 2j + 3k, b = 2i + 3j - 5k, and c = 3i - j + λ k be th… | JEE Main 2024 Mathematics PYQ

MCQMediumJEE Main 2024 · 8 April, Shift 2Dot Product

Let $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}$ , $\vec{b} = 2\hat{i} + 3\hat{j} - 5\hat{k}$ , and $\vec{c} = 3\hat{i} - \hat{j} + \lambda \hat{k}$ be three vectors. Let $\vec{r}$ be a unit vector along $\vec{b} + \vec{c}$ . If $\vec{r} \cdot \vec{a} = 3$ , then $3\lambda$ is equal to:

A
$27$
B
$25$
C
$30$
D
$21$

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