The angle subtended by the vector $\vec{A}=4 \hat{\imath}+3 \hat{\jmath}+12 \hat{k}$ with the $\mathrm{x}$…

The angle subtended by the vector $\vec{A}=4 \hat{\imath}+3 \hat{\jmath}+12 \hat{k}$ with the $\mathrm{x}$ -axis is
  1. $\sin ^{-1}\left(\frac{4}{13}\right)$
  2. $\cos ^{-1}\left(\frac{3}{13}\right)$
  3. $\cos ^{-1}\left(\frac{3}{13}\right)$
  4. $\sin ^{-1}\left(\frac{3}{13}\right)$

Solution

$\vec{A}=4 i+3 j+12 k$ $p=i$ $\cos \theta \frac{\mid \vec{A} \cdot \vec{B}}{|A||B|} \Rightarrow \frac{4}{\sqrt{16+9+144} \times 1}$ $\theta \begin{aligned} \Rightarrow \cos ^{-1} 1 / 13 & \end{aligned}$

Asked in: MHT CET 2020 (19 Oct Shift 2)

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