 Hello and welcome to this session. In this session we discussed the following question which says given vector A equal to 8i cap minus 2j cap plus 3k cap and vector B is equal to lambda i cap minus 2j cap plus 2k cap over values of lambda vector A plus vector B is orthogonal to vector A minus vector B. Before we move on to the solution let's recall the condition when two vectors are orthogonal to each other. Given vector A and vector B vector A is said to be orthogonal to vector B if vector A dot vector B is equal to 0. This is the key idea to be used in this question. Now we proceed with the solution. We are given a vector A is equal to 8i cap minus 2j cap plus 3k cap, vector B is equal to lambda i cap minus 2j cap plus 2k cap and we are given that vector A plus vector B is orthogonal to vector A minus vector B. That is vector A plus vector B dot vector A minus vector B is equal to 0. Let's put the values for vector A and vector B. So we have 8i cap minus 2j cap plus 3k cap plus lambda i cap minus 2j cap plus 2k cap dot 8i cap minus 2j cap plus 3k cap minus lambda i cap minus 2j cap plus 2k cap is equal to 0. This means we have 8 plus lambda i cap minus 4j cap plus 5k cap dot 8 minus lambda i cap plus 0j cap plus k cap is equal to 0. Now we take the dot product of these two vectors. So we get 8 plus lambda into 8 minus lambda plus 0 plus 5 is equal to 0. Further we have 64 minus 8 lambda plus 8 lambda minus lambda square plus 5 is equal to 0. That is 8 lambda minus 8 lambda cancels. We are left with minus lambda square plus 69 is equal to 0 or you can say further we have lambda square is equal to 69. This gives us lambda equal to plus minus 13. So the required values of lambda are plus minus 13. This is our final answer. This completes this session. Hope you have understood the solution of this question.