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Let’s check out your problem:

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

\newlineIf ∣a⃗+b⃗∣=∣a⃗−b⃗∣ |\vec{a}+\vec{b}|=|\vec{a}-\vec{b}| prove that a⃗ \vec{a} and b⃗ \vec{b} are perpendicular

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Full solution

Q. \newlineIf ∣a⃗+b⃗∣=∣a⃗−b⃗∣ |\vec{a}+\vec{b}|=|\vec{a}-\vec{b}| prove that a⃗ \vec{a} and b⃗ \vec{b} are perpendicular
  1. Calculate Magnitude Squares: Calculate the squares of the magnitudes of a⃗+b⃗\vec{a} + \vec{b} and a⃗−b⃗\vec{a} - \vec{b}.
  2. Expand Using Dot Products: Expand both sides using the property of dot products.
  3. Set Equal and Simplify: Set the expanded forms equal to each other and simplify.
  4. Solve for a⃗⋅b⃗\vec{a} \cdot \vec{b}: Solve for a⃗⋅b⃗\vec{a} \cdot \vec{b}.

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