 Hi and welcome to the session. Let's work out the following question. The question says using vectors prove that Coss a is equal to b squared plus c squared minus a squared divided by 2bc Let us see the solution to this question We see that in triangle a, b, c Wherein this angle is pi minus a this is pi minus b and this is pi minus c Here we have vector c Vector a, b is equal to vector c Vector b, c is equal to vector a and vector c, a is equal to vector b from triangular law of addition of vectors vector c, a plus vector a, b is equal to vector c, b This happens because Vector c, b is negative of vector b, c this implies vector b plus vector c is equal to minus vector a now Vector b plus vector c into vector b plus vector c is equal to minus vector a into minus vector a This is equal to vector a into vector a This implies mod of vector b plus vector c the whole square is equal to mod of vector a square This implies mod of vector b squared plus mod of vector c squared Plus twice of mod of vector b into mod of vector c is equal to Sorry, here we have just twice of vector b into vector c is Equal to mod of vector a square This implies mod of vector b squared plus mod of vector c squared Plus twice of mod of vector b into mod of vector c into cos pi minus a is equal to mod of vector a squared but Mod of vector a is equal to a mod of vector b is equal to b and Mod of vector c is equal to c Therefore v square plus c square minus 2 bc cos a is equal to a square hence cos a will be equal to v square plus c square minus a square divided by 2 vc Now this is what we were supposed to prove in this question I hope that you understood the solution and enjoyed the session. Have a good day