 Hi and welcome to the session. Let us discuss the following question, question says, find lambda and mu if 2i plus 6j plus 27k cross i plus lambda j plus mu k is equal to 0 vector. Let us now start with the solution. Now we are given 2i plus 6j plus 27k cross i plus lambda j plus mu k is equal to 0 vector. Now we know 0 vector has same initial and terminal point or we can say all the components of 0 vector are 0 only. Now we have to find values of lambda and mu. Now first of all we will find out cross product of these 2 vectors and we know cross product of these 2 vectors is given by determinant of unit vector i, unit vector j, unit vector k, 2 6 27 1 lambda mu and here we will write right hand side as it is. So here we can write is equal to 0 vector. Now expanding this determinant with respect to this row we get unit vector i multiplied by 6 mu minus 27 lambda minus unit vector j multiplied by 2 mu minus 27 plus unit vector k multiplied by 2 lambda minus 6 is equal to 0 vector. Now we know all the components of 0 vector are 0 only. So we can write unit vector i multiplied by 6 mu minus 27 lambda minus unit vector j multiplied by 2 mu minus 27 plus unit vector k multiplied by 2 lambda minus 6 is equal to 0 i plus 0 j plus 0 k. Now equating unit vector i, unit vector j and unit vector k on both the sides we get 6 mu minus 27 lambda is equal to 0 2 mu minus 27 multiplied by minus 1 is equal to 0. So here we can write minus 2 mu minus 27 is equal to 0. Similarly 2 lambda minus 6 is equal to 0. Now let us name these equations as equation 1, equation 2 and equation 3. Now from equation 3 we get lambda is equal to 6 upon 2 that is it is equal to 3. We know if we cancel common factor 2 from numerator and denominator both we get 3. So lambda is equal to 3. Now let us consider equation 2. From equation 2 we get minus 2 mu is equal to minus 27. Now dividing both the sides by minus 2 we get mu is equal to 27 upon 2. So this is the required value of lambda and this is the required value of mu. So this is our required solution. This completes the session. Hope you understood the solution. Take care. Have a nice day.