Physics Vectors & Equilibrium PMDC Conceptual Practice
PMDC Verified Question 44 of 50
If the expression \(0.8\hat{i} + 0.5\hat{j} + c\hat{k}\) represents a unit vector, find the value of the constant \(c\).
A
\(\sqrt{0.64}\)
B
0.20
C
\(\sqrt{0.11}\)
D
1.00
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: \(\sqrt{0.11}\)
Concept:
The magnitude of a unit vector is exactly equal to one.

Formula:
$$\sqrt{x^2 + y^2 + z^2} = 1$$

Solution:
Set the magnitude of the given vector to 1:
$$\sqrt{(0.8)^2 + (0.5)^2 + c^2} = 1$$
Square both sides of the equation:
$$0.64 + 0.25 + c^2 = 1$$
$$0.89 + c^2 = 1$$
$$c^2 = 1 - 0.89 = 0.11 \implies c = \sqrt{0.11}$$

Why other options are incorrect:
  • A is incorrect because it equals 0.8, which is the value of the x-component.
  • B and D are mathematically incorrect and do not satisfy the unit magnitude condition.

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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