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nevsk [136]
3 years ago
9

prove that if the sum and diffrence of two vectors are perpendicular then the vectors have equal magnitude?​

Physics
1 answer:
VikaD [51]3 years ago
5 0

Answer:

true.

Explanation:

Using the fact that the dot product of two perpendicular vectors is equal to zero:

(\overrightarrow{a}+\overrightarrow{b})\cdot (\overrightarrow{a}-\overrightarrow{b}) = 0\\\overrightarrow{a}\cdot\overrightarrow{a}-\overrightarrow{b}\cdot\overrightarrow{b}=0\\\overrightarrow{a}\cdot\overrightarrow{a}=\overrightarrow{b}\cdot\overrightarrow{b}\\|a|^2=|b|^2\\|a|=|b|

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