Question

resultant will be minimum if vectors are oppositly directed. ...true or false

Answer 1

The magnitude of adding of two vectors is given by...

l A +B l = √(A^2 + B^2 +2ABcos theta)

Here in right side to be minimum, the variable is cos theta.

So the magnitude will be minimum when maximum value will be substracted from A^2 +B^2.

So The maximum value of 2ABcos theta will be obtained when cos theta is minimum , that is at theta =180° .

If the angle between two vectors is 180° , then they will be in opposite direction.

so the value ...

lA+Bl =√(A^2+B^2+2ABcos180)
=√(A^2 + B^2 -2AB)
=√(A-B)^2