- #1

IonizingJai

- 14

- 0

__At what angles must be the two forces__

**Question:****##\vec A+\vec B##**and

**##\vec A-\vec B##**act so that the resultant may be :

**$$\sqrt{ A^2+B^2}$$**

*Attempt at solution :*Let the given forces be

**##\vec F_1=\vec A+\vec B##**and

**##\vec F_2=\vec A-\vec B##**.

Now, Resultant vector :

**##\vec F_1 + \vec F_2 = (\vec A+\vec B) + (\vec A-\vec B) ##**.

Magnitude of Resultant:

**##|\vec F_1 + \vec F_2| = \sqrt{(A+B)^2+(A-B)^2+2(A+B)(A-B)\cos(\theta)}##**.

Here,

**##\theta##**being the angle between

**##\vec F_1 and \vec F_2## .**

Stuck here ##=\sqrt{2(A^2+B^2)+2(A^2-B^2)\cos(\theta)}## .[ I'm noob with LaTeX too.].

Stuck here ##=\sqrt{2(A^2+B^2)+2(A^2-B^2)\cos(\theta)}## .