 Hi friends, I am Pooja and today we will discuss the following question. If either vector A is equal to zero or vector B is equal to zero then we have vector A dot vector B is equal to zero but the converse need not be true. Justify your answer with an example. Let us begin with the solution now. Now we have to show that the dot product of two vectors is equal to zero implies that the two vectors individually are not equal to zero. Now we know that if vector A dot vector B is equal to zero then this means that either vector A is perpendicular to vector B or vector A is equal to zero or vector B is equal to zero. Now we have to show that if vector A dot vector B is equal to zero then this implies vector A is not equal to zero and vector B is not equal to zero. That is we have to show vector A dot vector B is equal to zero implies A is perpendicular to B. So first let us consider vector A is equal to three i cap plus j cap plus two k cap and vector B is equal to i cap minus j cap minus k cap. Now we can clearly see that vector A is not equal to zero and vector B is not equal to zero and we will show that vector A dot vector B is equal to zero which will imply that vector A is perpendicular to vector B. Now vector A dot vector B is equal to now vector A is equal to three i cap plus j cap plus two k cap dot vector B is equal to i cap minus j cap minus k cap and we have this is equal to three into one which is equal to three one into minus one which is equal to minus one and two into minus one which is equal to minus two and we get this is equal to three minus three which is equal to zero. So we have got vector A dot vector B is equal to zero and we also have vector A is not equal to zero and vector B is not equal to zero. So we get this implies vector A is perpendicular to vector B. So we have shown that if the dot product of two vectors is equal to zero then it is not necessary that the two vectors individually are equal to zero. Hence we write our answer as take any two non-zero perpendicular vectors vector A and vector B. Hope you have understood the solution. Bye and take care.