Two forces have the same magnitude ?F?. What is the angle between the two vectors if their sum has a magnitude of (a) 2?? (b) (c) zero? Sketch the three vectors in each case.

Solution 1E Step 1 of 3: (a) 2F Two force having equal magnitude , F | 1 |= F| 2| = F . Here in the given case, the total net force is, F =2F | t| To have net force as 2F, F =tF + F 1 2 Both forces should be in same direction and parallel to each other, as shown below Therefore, angle between the two forces must be zero degree or 0 . 0 Step 2 of 3: (a) 2F Two force having equal magnitude , F | |= F| | = F . | 1 | | 2| Here in the given case, the total net force is, F = 2F | t| | | To have net force as 2F, Both forces should be right angle to each other, To calculate the resultant force, By pythagoras theorem, (F )t= (F ) + 1F )2 2 2 (F ) =(F ) +(F ) 2 2 t 1 2 2 2 (F )t= (F 1 + (F ) 2 Using F | 1 |= F| 2| = F | | | | |F = 2F | | 0 Therefore, angle between the two forces must be 90 .