 Good morning friends, I am Pudra and today we will discuss the following question. Evaluate the product 3 into vector A minus 5 into vector B dot product with 2 into vector A plus 7 into vector B. Let us now begin with the solution. So we have to find the dot product of 3 into vector A minus 5 into vector B and 2 into vector A plus 7 into vector B and we have this is equal to 3 into vector A dot 2 into vector A plus 3 into vector A dot 7 into vector B minus 5 into vector B dot 2 into vector A minus 5 into vector B dot 7 into vector B this is equal to 6 into mod of vector A square plus 21 into vector A dot vector B minus 10 into vector B dot vector A minus 35 into mod of vector B square and this is by distributive law. Now here 3 into 2 becomes 6 and vector A dot vector A becomes mod of vector A square here 3 into 7 becomes 21 and vector A dot vector B is written as it is. Here minus 5 into 2 becomes minus 10 and vector B dot vector A is written as it is and this is by distributive law. Here minus 5 into 7 becomes minus 35 and vector B dot vector B becomes mod of vector B square. This is equal to 6 into mod of vector A square plus 21 into vector A dot vector B minus 10 into vector A dot vector B and this is since vector B dot vector A is equal to vector A dot vector B minus 35 into mod of vector B square and we get this is equal to 6 into mod of vector A square now plus 21 into vector A dot vector B minus 10 into vector A dot vector B gives plus 11 into vector A dot vector B minus 35 into mod of vector B square. So we have got our answer as 6 into mod of vector A square plus 11 into vector A dot vector B minus 35 into mod of vector B square. Hope you have understood the solution. Bye and take care.