Question

show that the magnitude of resulting of two vectors,A and B lies in between A+B and A-B or B-A​

Answer 1

Answer:

Take two vectors a and b and complete the parallelogram. Let its area be [math]\: \Delta_1 \:[/math]. Now Draw vectors a+b and a-b and using them as adjacent sides complete their parallelogram. Let its area be [math]\: \Delta_2.[/math]

It is not difficult to see/prove [math]\: \Delta_2= 2 \Delta_1[/math].

Hence (a-b) X (a+b)= 2(a X b) (Why?)

Result will remain same if a and b are collinear vectors.