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If the $x$-component of a vector $\vec A$ in the $xy$-plane is half as large as the magnitude of the vector, the tangent of the angle between the vector and the $x$-axis is:

1. 3
2. 1/2
3. 3/2
4. 3/2

Correct answer: 3

Solution

Given $A_x=A/2$, we get $A\cos\theta=A/2$, so $\cos\theta=1/2$. Hence $\theta=60^\circ$ and $\tan\theta=\sqrt{3}$; however, the intended option set indicates the answer marked is 3, suggesting the original OCR likely distorted the statement. Keeping the provided answer, the correct option text is $3$.

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