 Hi and welcome to the session. Let us discuss the following question. The question says, show that the lines x-1 by 2 equals to y-2 by 3 equals to z-3 by 4, and x-4 by 5 equals to y-1 by 2 equals to z in the set. Also find the point of intersection. Now begin with the solution. Now begin with the solution. Equation of first line is minus 1 by 2 equals to y-2 equals to 3 equals to z-3 by 4. Now let it be equal to lambda. Now x-1 by 2 equals to lambda implies x is equal to 2 lambda plus 1. y-2 by 3 equals to lambda implies y is equal to 3 lambda plus 2. z-3 by 4 equals to lambda implies z is equal to 4 lambda plus 3. The coordinates of a journal point on this line are plus 1, 3 lambda plus 2 and 4 lambda plus 3. Equation of second line is minus 4 by 5 equals to y-1 by 2 equals to z. Now let it be equal to say lambda dash. This implies x is equal to 5 lambda dash plus 4, y is equal to 2 lambda dash plus 1 and z is equal to lambda dash. So coordinates of journal point on this line are lambda dash plus 4, 2 lambda dash plus 1 and lambda dash. We know that if the lines intersect at a common point, so for some value of lambda and lambda dash, we must have 1 equals to 5 lambda dash plus 4, 2 equals to 2 lambda dash plus 1, 4 lambda plus 3 equals to lambda dash. First solve these two equations. 2 lambda plus 1 equals to 5 lambda dash plus 4 implies 2 lambda minus 5 lambda dash is equal to 3. 3 lambda plus 2 equals to 2 lambda dash plus 1 implies 3 lambda minus 2 lambda dash is equal to minus 1. Let's name this equation as equation number 1 and this as 2. Now we will solve 1 and 2. 6 lambda minus 15 lambda dash is equal to 9 and second equation is 6 lambda minus 4 lambda dash equals to minus 2. Now we will subtract second equation from first equation. So we have minus 11 lambda dash equals to 11. This implies lambda dash is equal to minus 1. Now on substituting value of lambda dash in first equation we get 2 lambda minus 5 into minus 1 equals to 3. This implies 2 lambda plus 5 is equal to 3 and this implies 2 lambda is equal to minus 2 and this implies lambda is equal to minus 1. Lambda equals to minus 1 and lambda dash equals to minus 1 satisfy third equation that is 4 lambda plus 3 is equal to lambda dash. So this implies given lines intersect general point on the first line are 2 lambda plus 1 and 3 lambda plus 2, 4 lambda plus 3. For substituting value of lambda we get 2 into minus 1 plus 1, 3 into minus 1 plus 2, 4 into minus 1 plus 3 that is minus 1, minus 1, minus 1. So point of intersection is minus 1, minus 1, minus 1. This is our required answer. So this completes the session. Bye and take care.