 Hello and welcome to the session. In this session we discussed the following question which says write the value of P for which vector A equal to 3i cap plus 2j cap plus 9k cap and vector B equal to i cap plus pj cap plus 3k cap are parallel vectors. We know the condition for the vectors A and B to be parallel vectors is vector A cross vector B is equal to 0 vector. That is we have vector A and vector B are parallel vectors if vector A cross vector B is equal to 0 vector. This is the key idea that we use for this question. Let's move on to the solution now. We are given a vector A equal to 3i cap plus 2j cap plus 9k cap and vector B is equal to i cap plus pj cap plus 3k cap. We have to find the value for P such that we have vector A and vector B are parallel vectors. Let's first find out vector A cross vector B this is equal to determinant i cap j cap k cap then in the first row we write the scalar components of vector A which is 3, 2, 9 then in the second row we write the scalar components of vector B which is 1, p, 3. Now this is equal to i cap into 2 multiplied by 3 which is 6 minus 9 multiplied by p that is 9p minus j cap into 3 multiplied by 3 that is 9 minus 9 multiplied by 1 which is 9 plus k cap into 3 multiplied by p that is 3p minus 2 multiplied by 1 that is 2 and so this is further equal to 6 minus 9p i cap minus 0 into j cap plus 3p minus 2k cap. So this is vector A cross vector B. Now since vector A and vector B are the parallel vectors therefore vector A cross vector B is equal to 0 vector that is 6 minus 9p i cap minus 0 j cap plus 3p minus 2 k cap is equal to 0 vector that is 6 minus 9p i cap minus 0 j cap plus 3p minus 2 k cap is equal to 0 i cap plus 0 j cap plus 0 k cap. We equate the scalar components and we get 6 minus 9p is equal to 0 or 3p minus 2 is equal to 0. So we have 9p is equal to 6 which gives us p is equal to 6 upon 9. Now 3, 2 times is 6 and 3, 3 times is 9 therefore we get p is equal to 2 upon 3 and in this case also we get p is equal to 2 upon 3. Thus the final value of p is equal to 2 upon 3. This is our final answer. So this completes the fashion. Hope you have understood the solution of this question.