Question

Resultant of two vectors A and B is given by |R|={|A|-|B|}, angles between A and B will be

Answer 1

the angle is not fix as the value of A and B is not given
but I had a formula to calculate the angle

Answer 2

Answer:

180 ° is the required angle between A and B

Explanation:

Given , Resultant of two vectors A and B is ,

| R | = {|A| - |B|}

And we know that  Resultant of two vector is ,

R = $\sqrt{A^2 + B^2 + 2AB cos \theta }$

Where , A and B are two vector and $\theta$ be the angle between them .

Now , according to the question we have ,

|R| = {|A| -|B|} = $\sqrt{|A|^{2} + |B|^{2} + 2AB cos\theta}$

Squaring both side  we get  ,

$|R|^{2}$ = $(|A|-|B|)^{2} =\sqrt{( |A|^{2} + |B|^{2} + 2AB cos\theta)}^2$

⇒$(|A|^{2} + |B|^{2} - 2AB )$ = ${|A|^{2} + |B|^{2} + 2AB cos\theta}$

⇒-1 = $cos\theta$            

⇒ $\theta$ = 180 °                   [Where the value of  cos 180 = -1 ]

Final answer :

Hence , the angle between A and B is 180  °

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