Physics Vectors & Equilibrium PMDC Conceptual Practice
PMDC Verified Question 10 of 50
The unit vector \(\hat{a}\) in the direction of vector \(\vec{a}\) is mathematically defined as:
A
\(|\vec{a}|\)
B
\(\vec{a} \cdot \vec{a}\)
C
\(\vec{a} \times \vec{a}\)
D
\(\vec{a} / |\vec{a}|\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: \(\vec{a} / |\vec{a}|\)
Concept:
Mathematical definition of a unit vector.

Formula:
$$\hat{a} = \frac{\vec{a}}{|\vec{a}|}$$

Solution:
A unit vector is a vector that has a magnitude of exactly 1 and points in the same direction as the original vector. It is obtained by dividing the vector \(\vec{a}\) by its scalar magnitude \(|\vec{a}|\).

Why other options are incorrect:
  • A is incorrect because \(|\vec{a}|\) is a scalar magnitude, not a vector.
  • B is incorrect because the dot product \(\vec{a} \cdot \vec{a}\) yields a scalar equal to \(|\vec{a}|^2\).
  • C is incorrect because the cross product of any vector with itself is always the null vector.

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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