 Hello and welcome to the session. In this session we discuss the following question which says for what value of lambda are the vectors vector a equal to 2i cap is lambda j cap plus k cap and vector b equal to i cap minus 2j cap plus 3k cap perpendicular to each other. Let's move on to the solution. We have vector a equal to 2i cap plus lambda j cap plus k cap and vector b equal to i cap minus 2j cap plus 3k cap. Now we have that vector a and vector b are perpendicular to each other. So we have vector a dot vector b is equal to 0. Now vector a dot vector b is equal to 2i cap plus lambda j cap plus k cap dot i cap minus 2j cap plus 3k cap. So this is equal to 2 minus 2 lambda plus 3 that is we get the vector a dot vector b is equal to minus 2 lambda plus 5. Now we have vector a dot vector b is equal to 0 therefore minus 2 lambda plus 5 equal to 0. Now from here we get minus 2 lambda is equal to minus 5 that is we have lambda is equal to 5 upon 2. Thus our final answer is for lambda equal to 5 upon 2 vector a equal to 2i cap plus lambda j cap plus k cap and vector b equal to i cap minus 2j cap plus 3k cap are perpendicular to each other. This completes the session. Hope you have understood the solution for this question.