Question

Q3) The |+ | =| |+| |, then angle between and will be​

Answer 1

Answer:

If |A+B|=|A|+|B|, then what is the angle between A and B?

For two vectors A⃗ and B⃗ , the angle between them being θ , the magnitude of the resultant vector A+B→ is given by,

|A+B|=|A|2+|B|2+2|A||B|cosθ−−−−−−−−−−−−−−−−−−−−√

Now in the problem we've,

|A+B|=|A|+|B|

Squaring on both sides,

|A+B|2=(|A|+|B|)2

∴|A|2+|B|2+2|A||B|cosθ=|A|2+|B|2+2|A||B|

∴cosθ=1 ,

assuming neither of the vectors are zero vectors.

∴θ=0

Thus the two vectors must be aligned in the same direction.

Hope it helps!