When two vectors magnitudes A and B are inclined at angle theta, the magnitude of their resultant is 2A - Physics - Basic Mathematics(Pre-requisite)

Question

When two vectors magnitudes A and B are inclined at angle theta,
the magnitude of their resultant is 2A If the first vector is
doubled, the magnitude of resultant become 3A Find the ratio of A?
to B?

Vaibhav Tiwari · Accepted Answer

Dear Student,

R2=A2+B2+2ABcosθ2A2=A2+B2+2ABcosθ4A2=A2+B2+2ABcosθ3A2=B2+2ABcosθB2=3A2-2ABcosθ   
 1Now,R'2=2A2+B2+22ABcosθ3A2=4A2+B2+4ABcosθ5A2=B2+4ABcosθ  B2=5A2-4ABcosθ 
 2from 1 and 23A2-2ABcosθ=5A2-4ABcosθ2A2=2ABcosθAB=cosθ
Regards

When two vectors magnitudes A and B are inclined at angle theta, the magnitude of their resultant is 2A. If the first vector is doubled, the magnitude of resultant become 3A. Find the ratio of A? to B?.