 I am welcome to the session and since that's the polling question, the question says if A, B, C are the lengths of the sides opposite respectively to angles A, B, C of triangle A, B, C using vectors prove that cos C is equal to A squared plus B squared minus C squared divided by 2 A, B. And this is the triangle A, B, C and we are given that A, B and C are the lengths of the sides opposite to angles A, B and C and we have to prove that cos C is equal to A squared plus B squared minus C squared divided by 2 A, B. Let's now begin with the solution. Let vector B, C is equal to the C, A is equal to vector B, A, B is equal to vector C. Now magnitude of vector A is equal to magnitude of vector B, C and this is equal to A, magnitude of vector B is equal to magnitude of vector C, A and this is equal to v. Similarly, magnitude of vector av is equal to magnitude of vector c and this is equal to c. Now by triangular law of addition, vc plus vector ca is equal to vector va, vc plus vector ca is equal to minus vector av. Now vector vc is equal to vector a and vector ca is equal to vector b, vector av is equal to vector c. A plus vector v dot vector v is equal to minus vector v to magnitude of vector a into magnitude of vector v into.