Which of the following are legitimate mathematical operations: In each case, give the reason for your answer.

Solution to 22DQ. Here we will check the legitimacy of the given vector equations one by one. Part 1 Step 1 is subtraction between two vectors. Thus the subtraction between two vectors gives you a vector quantity. is the dot product between two vectors. Step 2 Let Thus Thus this equation is legitimate. Part 2 Step 1 Here is the subtraction between two vectors and . This quantity is a vector quantity. is the dot product between two products. Step 2 Let = , then is equal to , which is the vector product of two quantities. The cross product or vector product will give a vector quantity. Thus this equation is also legitimate. Part 3 Step 1 is the cross product between two vectors. The result is always a vector. We know that a dot product is a scalar product between two vectors, whose result is a scalar quantity. Step 2 Let Thus Which is a legitimate equation. Part 4 Step 1 is a vector product between two vectors whose reslut is also a vector quantity. Step 2 Let Then Thus it is a legitimate equation. Part 4 Step 1 Here which is a scalar product giving a scalar quantity.