if |A|=|B|=|A-B|, then find the angle b/w the two vectors

Asked by kaziryan.05 | 13th Apr, 2022, 09:01: PM

Expert Answer:

Let begin mathsize 14px style stack O P with rightwards arrow on top end style = begin mathsize 14px style A with rightwards arrow on top end style  and begin mathsize 14px style stack O Q with rightwards arrow on top end style = begin mathsize 14px style B with rightwards arrow on top end style  . Let θ be the angle between the vectors begin mathsize 14px style A with rightwards arrow on top end style and begin mathsize 14px style B with rightwards arrow on top end style
We can construct  begin mathsize 14px style stack O S with rightwards arrow on top end style =  ( begin mathsize 14px style A with rightwards arrow on top end style - begin mathsize 14px style B with rightwards arrow on top end style ) as shown in figure.
OSPQ is parallelogram and PQ = | ( begin mathsize 14px style A with rightwards arrow on top end style - begin mathsize 14px style B with rightwards arrow on top end style ) | 
As per the given condition , | begin mathsize 14px style A with rightwards arrow on top end style | = | begin mathsize 14px style B with rightwards arrow on top end style | = | ( begin mathsize 14px style A with rightwards arrow on top end style - begin mathsize 14px style B with rightwards arrow on top end style ) |  , all the sides of ΔOPQ are same .
Hence θ = 60o = ( π / 3 ) rad
 
Hence angle between begin mathsize 14px style A with rightwards arrow on top end style and begin mathsize 14px style B with rightwards arrow on top end style is 60o or ( π / 3 ) rad

Answered by Thiyagarajan K | 13th Apr, 2022, 09:39: PM