Physics Vectors & Equilibrium PMDC Conceptual Practice
PMDC Verified Question 8 of 50
What is the cross product of the unit vectors \(\hat{i} \times \hat{j}\)?
A
0
B
-\(\hat{j}\)
C
-\(\hat{k}\)
D
\(\hat{k}\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: \(\hat{k}\)
Concept:
Cyclic permutation of Cartesian unit vectors in cross products.

Solution:
For the orthogonal unit vectors, the cross product of any two yields the third. The standard positive direction follows the cyclic order: \(\hat{i} \rightarrow \hat{j} \rightarrow \hat{k} \rightarrow \hat{i}\).
Therefore:
$$\hat{i} \times \hat{j} = \hat{k}$$

Why other options are incorrect:
  • A is incorrect because \(\hat{i}\) and \(\hat{j}\) are orthogonal, meaning their cross product is at maximum magnitude (1), not zero.
  • B and C are incorrect because they represent the wrong directions. Only a positive \(\hat{k}\) points in the direction determined by the right-hand rule.

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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