 Hi, and welcome to the session. Let us discuss the following question. The question says, show that the lines x minus 1 divided by 2 equals to y minus 2 divided by 3 equals to z minus 3 divided by 4, and x minus 4 divided by 5 equals to y minus 1 divided by 2 equals to z in the set. Also find the point of intersection. Let's now begin with the solution. Equation of first line is divided by 2 equals to y minus 2 divided by 3 equals to z minus 3 divided by 4. Let it be equal to say lambda. Now, x minus 1 divided by 2 equals to lambda implies x is equal to 2 lambda plus 1. Similarly, we can say that y is equal to 3 lambda plus 2, and z is equal to 4 lambda plus 3. So coordinates of a general point, this line now, plus 1, 3 lambda plus 2, and 4 lambda plus 3. Now, equation of second line is equals to y minus 1 by 2 equals to z. We can write z as z minus 0 by 1. Let it be equal to say mu. This implies x is equal to 5 mu plus 4. y is equal to 2 mu plus 1. And z is equal to mu. So we can say that coordinates of a general point on second line are mu plus 4 plus 1 and mu. So for some value of lambda and mu plus 1 equals to 5 mu plus 4, 3 lambda plus 2 equals to 2 mu plus 1 plus 3 equals to mu. Now, 2 lambda plus 1 equals to 5 mu plus 4 implies 2 lambda minus 5 mu is equal to 3. 3 lambda plus 2 equals to 2 mu plus 1 implies 3 lambda minus 2 mu is equal to minus 1. Plus 3 equals to mu implies 4 lambda minus mu is equal to minus 3. Let us name this as equation number 1. This has 2, and this has 3. We call equation 1 and 2. Equation minus 2 lambda minus 5 mu equals to 3. And equation 2 is 3 lambda minus 2 mu equals to minus 1. Multiply this equation by 3 and this by 2. So we get 6 lambda equals to 9. Then we have 6 lambda minus 4 mu equals to minus 2. Now, subtract this equation from this equation. So we have minus 11 mu equals to 11. And this implies mu is equal to minus 1. Now, 2 lambda minus 5 mu is equal to 3. Substitute the value of mu here. And thus we get 2 lambda minus 5 into minus 1 equals to 3. This implies 2 lambda is equal to 3 minus 5. And this implies lambda is equal to minus 1. Now, since 2 equals to minus 1 and mu equals to minus 1, satisfy third equation. Therefore, the given lines intersect. They're equals to minus 1 in 2 lambda plus 1, 3 lambda plus 2, and 4 lambda plus 3. By substituting value of lambda, we get coordinates of required point as minus 1, minus 1, minus 1. This is how required answer. So this completes the session. Bye and take care.