Physics Vectors & Equilibrium PMDC Conceptual Practice
PMDC Verified Question 49 of 50
If \(\vec{A} + \vec{B} = 7\hat{i} + 7\hat{k}\) and \(\vec{A} - \vec{B} = -\hat{i} + \hat{k}\), what is the scalar magnitude of vector \(\vec{A}\)?
A
3
B
5
C
7
D
10
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: 5
Concept:
Solving systems of vector equations.

Solution:
Step 1: Add the two vector equations together to eliminate \(\vec{B}\):
$$(\vec{A} + \vec{B}) + (\vec{A} - \vec{B}) = (7\hat{i} + 7\hat{k}) + (-\hat{i} + \hat{k})$$
$$2\vec{A} = 6\hat{i} + 8\hat{k}$$
$$\vec{A} = 3\hat{i} + 4\hat{k}$$
Step 2: Calculate the scalar magnitude of vector \(\vec{A}\):
$$|\vec{A}| = \sqrt{3^2 + 0^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$$

Why other options are incorrect:
  • 3, 7, and 10 are incorrect magnitudes that result from mathematical errors (such as using \(3 + 4 = 7\) instead of the square root of the sum of squares, or failing to divide by 2).

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.

Previous Question All Vectors & Equilibrium MCQs Next Question

Want to solve full-length papers under timed exam conditions?

Practice with zero-scroll lockdown sprints, dynamic latency zone timers, live peer selection telemetry, and the automated Amber mistake recovery loop.

Enter Arena Sprint iOS App Android App