Question

what is the angle between a bar and b bar when modules of a bar . b bar =modules o a bar and b bar

Answer 1

Explanation:

Let a⃗ ,b⃗ 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∘ .