 Good morning friends, I am Purva and today we will solve the following question find the projection of the vector i cap minus j cap on the vector i cap plus j cap Let us now begin with the solution Let us denote i cap minus j cap by vector a and i cap plus j cap by vector b so let Vector a is equal to i cap minus j cap and vector b is equal to i cap plus j cap now the projection of vector a on vector b is given by vector a dot vector b upon mod of vector b Now we have vector b is equal to i cap plus j cap so mod of vector b is equal to under root of 1 square plus 1 square Which is equal to under root of 1 plus 1 which is equal to root 2 so mod of vector b is equal to root 2 therefore we have projection of vector a on vector b is Equal to vector a that is i cap minus j cap Dot vector b that is i cap plus j cap upon mod of vector b which is equal to root 2 This is equal to now the dot product of i cap minus j cap and i cap plus j cap is 1 into 1 that is 1 plus minus 1 into 1 that is minus 1 upon root 2 and we get this is equal to 1 minus 1 upon root 2 Which is equal to 0 So the projection of vector a on vector b is Zero this is our answer. Hope you have understood the solution. Bye and take care