Question

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

Answer 1

Answer:

true.

Explanation:

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

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