Question

if A bar and B bar are vectors such that |A+B| = |A-B|, then the angle between A bar and B bar is​

Answer 1

Explanation:

Solution

Let a→,b→ are the two vectors .

Sum of vectors

=a¯+b¯=a2+b2+2abcosθ−−−−−−−−−−−−−−−√

Difference of vectors

=a¯−b¯=a2+b2−2abcosθ−−−−−−−−−−−−−−−√

Given ∣∣a¯+b¯∣∣=∣∣a¯−b¯∣∣

⇒a2+b2+2abcosθ−−−−−−−−−−−−−−−√

=a2+b2−2abcosθ−−−−−−−−−−−−−−−√

by squaring on both sides ,

a2+b2+2abcosθ=a2+b2−2abcosθ

∴ 4 ab cos θ=0 or θ=90∘

So if ∣∣a¯+b¯∣∣=∣∣a¯−b¯∣∣ then angle between a¯ and b¯is90∘ .

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