 Hi and welcome to the session. I am Deepika here. Let's discuss the question using the property of determinants. And without expanding, prove that determinant x ax plus a yp y plus b z c z plus c is equal to 0. Let's start the solution. Let delta is equal to a given determinant that is x ax plus a y b y plus b z c z plus c. We will use the properties of determinants and we will prove that delta is equal to 0. By applying 3 goes to c3 minus c2 we get delta is equal to y z a b c c3 is c3 minus c2. So x plus a minus a is equal to x y plus b minus b is y z plus c minus c is z. Now delta is equal to 0 as two columns c1 and c3 are identical because we have the property as if any two rows or columns of a determinant are identical that is all corresponding elements are same then value of determinant is 0. Hence we have proved that delta is equal to 0 hence prove. I hope the question is clear to you. Bye and have a good day.