Question 112: Motion in 2D & Vectors

Question

The angle subtended by the vector $A=4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+12 \hat{\mathbf{k}}$ with the $X$-axis is

Accepted Answer

Given, $\mathbf{A}=4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+12 \hat{\mathbf{k}}$
$$\begin{aligned}
& 	ext { Also, } \mathbf{A}=\mathbf{A}_x+\mathbf{A}_y+\mathbf{A}_z \
& \Rightarrow A_x=4
\end{aligned}$$
The angle subtended by vector $\mathbf{A}$ with $X$-axis is
$$\begin{aligned}
\cos \phi & =\frac{A_x}{|A|}=\frac{4}{\sqrt{4^2+3^2+12^2}} \
\cos \phi & =\frac{4}{13} \
\phi & =\cos ^{-1}\left(\frac{4}{13}ight)
\end{aligned}$$

Answer

$\cos ^{-1}\left(\frac{3}{13}\right)$

Answer

$\sin ^{-1}\left(\frac{3}{13}\right)$

Answer

$\sin ^{-1}\left(\frac{4}{13}\right)$

Answer

$\cos ^{-1}\left(\frac{4}{13}\right)$

Motion in 2D & Vectors

The angle subtended by the vector A=4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+12 \hat{\mathbf{k}} with the X-axis is

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