Physics Vectors & Equilibrium PMDC Conceptual Practice
PMDC Verified Question 47 of 50
If the rectangular x-component of a vector is \(\sqrt{3}\) and its y-component is 1, what is the angle made by the vector with the positive x-axis?
A
\(60^\circ\)
B
\(30^\circ\)
C
\(45^\circ\)
D
\(90^\circ\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \(30^\circ\)
Concept:
Calculating vector direction from its rectangular components.

Formula:
$$\tan\theta = \frac{A_y}{A_x}$$

Solution:
Substitute the component values into the formula:
$$\tan\theta = \frac{1}{\sqrt{3}}$$
$$\theta = \arctan\left(\frac{1}{\sqrt{3}}\right) = 30^\circ$$

Why other options are incorrect:
  • \(60^\circ\): This angle would swap the components, making the x-component 1 and the y-component \(\sqrt{3}\).
  • \(45^\circ\): Requires equal components (e.g. 1 and 1).
  • \(90^\circ\): Requires the x-component to be zero.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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