 Good morning friends. I am Purva and today we will discuss the following question. If vector a dot vector a is equal to 0 and vector a dot vector b is equal to 0 then what can be concluded about the vector b? Let us now begin with the solution. Now we are given that vector a dot vector a is equal to 0. Now from this we can clearly see that this implies vector a is equal to 0 because the dot product of a vector with itself is equal to 0 means the vector itself is equal to 0 and we are also given that vector a dot vector b is equal to 0. Now the dot product of two vectors is equal to 0 means that either the two vectors are perpendicular to each other or either one of them is equal to 0. So we have this implies either vector a is perpendicular to vector b or we have vector a is equal to 0 or vector b is equal to 0. Now we mark this as equation 1 and this as equation 2. So from 1 and 2 we have vector a is equal to 0 and either vector a is perpendicular to vector b or vector a is equal to 0 or vector b is equal to 0. So now we have got vector a is equal to 0. So putting here vector a is equal to 0 and vector b has any vector we will get the dot product of vector a and vector b as 0. So we get this implies vector b is any vector. Hence we write our answer as vector b can be any vector. Hope you have understood the solution. Bye and take care.