 Good morning friends, I am Purva and today we will work out the following question. In triangle ABC, which of the following is not true? A, vector AB plus vector BC plus vector CA is equal to zero vector, B, vector AB plus vector BC minus vector AC is equal to zero vector, C, vector AB plus vector BC minus vector CA is equal to zero vector, D, vector AB minus vector CB plus vector CA is equal to zero vector. Let us consider a situation that a girl moves from point A to B and then from B to C. Then the net displacement made by the girl from point A to point C is given by the vector AC. So we have vector AC is equal to vector AB plus vector BC. So this is known as triangle law of vector addition and this is the key idea which we will use to solve this question. Now in this question we will show that in which out of the following ABC and D does the triangle law of addition hold. So let us begin with the solution now. Now in A part we are given vector AB plus vector BC plus vector CA is equal to zero vector. Now this implies we can write this as vector AB plus vector BC is equal to minus vector CA. We can also write this as this implies vector AB plus vector BC is equal to now minus vector CA is equal to vector AC. So we have this is equal to vector AC. So from key idea we can clearly see that triangle of addition holds in part A. So we write part A is true A is true as triangle law of addition holds. Now we consider part B and we are given vector AB plus vector BC minus vector AC is equal to zero vector. Now we can write this as this implies vector AB plus vector BC is equal to vector AC and this is triangle law of addition. So we have B is true as triangle law of addition holds. Now part C is vector AB plus vector BC minus vector CA is equal to zero vector. Now we can write this as this implies vector AB plus vector BC is equal to vector CA. Now since vector CA is equal to minus vector AC. So we have this implies vector AB plus vector BC is equal to minus vector CA. Now the triangle law of addition does not hold in this part. So we have C is not true as triangle law of addition does not hold. Now D part is vector AB minus vector CB plus vector CA is equal to zero vector and we can write this as this implies vector AB minus vector CB is equal to minus vector CA. Now since minus vector CA can be written as vector AC and minus vector CB can be written as vector BC. Therefore we have this implies vector AB plus vector BC is equal to vector AC which is again triangle law of addition. So we have D is true as triangle law of addition holds. Hence only C is not true. So we get our answer as C. Hope you have understood the solution. Bye and take care.