Question

two vectors A and B are given such that B=A/2. The maximum angle between A vector and A+B vector will be - ​

Answer 1

two vectors A and B are given such that B=A/2. The maximum angle between A vector and A+B vector will be - ​

Explanation:

(A+B).(A−B)=|A+B|∗|A−B|∗cosϕ  

=>|A|2+A.B−A.B−|B|2=(|A|2+|B|2+2ABcosθ−−−−−−−−−−−−−−−−−−−√)(|A|2+|B|2+2ABcosθ−−−−−−−−−−−−−−−−−−−√)∗cosϕ

=>|A|2−|B|2=(|A|2+|B|2+2ABcosθ)(|A|2+|B|2−2ABcosθ)−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√∗cosϕ

=>|A|2−|B|2=(|A|2+|B|2)2−(2ABcosθ)2−−−−−−−−−−−−−−−−−−−−−−−√∗cosϕ

=>|A|2−|B|2=|A|4+|B|4+2|A|2|B|2–4|A|2|B|2cos2θ−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√∗cosϕ

=>|A|2−|B|2=|A|4+|B|4+2|A|2|B|2(1–2cos2θ)−−−−−−−−−−−−−−−−−−−−−−−−−−−√∗cosϕ

=>|A|2−|B|2=|A|4+|B|4+2|A|2|B|2(−cos2θ)−−−−−−−−−−−−−−−−−−−−−−−−−−√∗cosϕ

=>|A|2−|B|2=|A|4+|B|4−2|A|2|B|2cos2θ−−−−−−−−−−−−−−−−−−−−−−−√∗cosϕ

=>cosϕ=|A|2−|B|2|A|4+|B|4−2|A|2|B|2cos2θ−−−−−−−−−−−−−−−−−−−−−−−√