 Hello and welcome to the session. In this session we discussed the following question which says find the values of lambda so that the lines 1 minus x upon 3 equal to 7 y minus 14 upon 2 lambda is equal to 5 z minus 10 upon 11 and 7 minus 7x upon 3 lambda is equal to y minus 5 upon 1 is equal to 6 minus z upon 5 are perpendicular to each other. Before we move on to the solution, let's recall the conditions for which the two lines are perpendicular to each other. Consider a line l1 whose equation is x minus x1 upon a1 is equal to y minus y1 upon b1 is equal to z minus z1 upon c1 and a line l2 with equation x minus x2 upon a2 is equal to y minus y2 upon b2 is equal to z minus z2 upon c2. Now line l1 has direction ratios a1 b1 c1 that is we have a1 b1 c1 are the direction ratios of the line l1 and a2 b2 c2 are the direction ratios of the line l2 line l1 and line l2 are perpendicular to each other if we have a1 a2 plus b1 b2 plus c1 c2 is equal to 0. This is the key idea that we use for this question. Let's proceed with the solution now. The given equations of the lines are 1 minus x upon 3 is equal to 7y minus 14 upon 2 lambda is equal to 5 z minus 10 upon 11. Let this be equation 1 and the other equation of the line is 7 minus 7x upon 3 lambda is equal to y minus 5 upon 1 is equal to 6 minus z upon 5. Let this be equation 2. Now let's write equation 1 and equation 2 in standard form as these equations. Now writing the given equations in standard form we get minus 1 upon minus 3 is equal to y minus 2 upon 2 lambda by 7 is equal to z minus 2 upon 11 upon 5. Let this be equation 3. Now let's write the equation 2 in the standard form and we get x minus 1 upon minus 3 lambda by 7 is equal to y minus 5 by 1 is equal to z minus 6 upon minus 5. Now comparing equations 3 and 4 by the standard equations of the line given in the key idea we get a1 is equal to minus 3 b1 is equal to 2 lambda by 7 and c1 is equal to 11 upon 5. Now from equation 4 we have a2 is equal to minus 3 lambda by 7 b2 is equal to 1 and c2 is equal to minus 5. Now since we have the given lines by the equations 1 and 2 are perpendicular therefore we have the condition a1 a2 plus b1 b2 plus c1 c2 is equal to 0. Now substituting the respective values of a1 b1 c1 a2 b2 c2 we get minus 3 into minus 3 lambda by 7 2 lambda by 7 into 1 plus 11 upon 5 into minus 5 is equal to 0. So this gives us 9 lambda by 7 plus 2 lambda by 7 plus now this 5 and 5 cancels so we have minus 11 is equal to 0. So this gives us 9 lambda plus 2 lambda by 7 minus 11 is equal to 0 or you can say we have 11 lambda by 7 minus 11 is equal to 0. This gives us 11 lambda upon 7 is equal to 11 from here we get the value of lambda as 11 into 7 upon 11. Now this 11 and 11 cancels therefore we get the value of lambda as 7. So this is the required value of the lambda this completes the session hope you have understood the solution of this question.