Question
The sum of two vectors, $\vec{A}+\vec{B},$ is perpendicular to their difference, $\vec{A}-\vec{B}$. How do the vectors' magnitudes compare?
Step 1
This means that the dot product of these two vectors is zero, i.e., $(\vec{A}+\vec{B}) \cdot (\vec{A}-\vec{B}) = 0$. Show more…
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Prove that two vectors must have equal magnitudes if their sum is perpendicular to their difference.
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Vector Analysis
Round 1
Show that if two nonparallel vectors have the same magnitude, their sum must be perpendicular to their difference.
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