When the vector sum of the two forces is perpendicular to their vector difference?

The two diagonals of a parallelogram formed by two vectors represent the vector sum and vector difference of two vectors. 
When the parallelogram is a square, the diagonals are perpendicular. Then, the two force vectors are represented by the adjacent sides of the square. Hence, the two force vectors which are equal in magnitude and perpendicular to each other have their vector sum perpendicular to their vector difference.
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A particle in motion is under the action of four forces such that these forces are represented by the four sides of quadrilateral taken in order. What type of motion the particle undergoes? 

The resultant force of the four forces, represented by four sides of a quadrilateral, taken in order is zero. Thus, the particle does not experience any force and the particle moves with constant velocity. 
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How can you explain that the flying of a bird is an example of resultant of two vectors? 


Flying of a bird is an example of resultant of two vectors.

i) When the bird flies, it strikes the air with wings A and B towards O along  

ii) Action and reaction are opposite. Therefore, the air strikes the wings in opposite direction i.e. along .

iii) The resultant of these vectors is in the upward direction which balances the weight of the bird.

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Can three vectors not in one plane give a zero resultant? Can four vectors also do? 

The resultant of the two vectors lie in the same plane. Hence, three vectors in single plane cannot give the resultant zero. For the resultant of three vectors to be zero, resultant of two should be equal and opposite to the third. 
Here, since the three vectors do not lie in the same plane, the resultant of the two cannot be in opposite direction of the third, hence resultant can not be zero. 

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Does the scalar quantity remain conserved in a process? Give example in support of your answer.

A scalar quantity need not remain conserved in the process.

For example, during the adiabatic compression, temperature, which is a scalar quantity does not remain conserve while mass, a scalar quantity, remains conserved. 
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