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If
| vec(a)+ vec(b)|=| vec(a)- vec(b)| prove that
vec(a) and
vec(b) are perpendicular.

$\newline$ If $|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|$ prove that $\vec{a}$ and $\vec{b}$ are perpendicular

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Even and odd functions

Full solution

Q.

\newline

If

|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|

prove that

\vec{a}

and

\vec{b}

are perpendicular

Calculate Magnitude Squares: Calculate the squares of the magnitudes of $\vec{a} + \vec{b}$ and $\vec{a} - \vec{b}$ .
Expand Using Dot Products: Expand both sides using the property of dot products.
Set Equal and Simplify: Set the expanded forms equal to each other and simplify.
Solve for $\vec{a} \cdot \vec{b}$ : Solve for $\vec{a} \cdot \vec{b}$ .

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