 Hi and welcome to our session. Let us just ask the following question. The question says, if magnitude of vector a is equal to 5, magnitude of vector b is equal to 30, and magnitude of vector a cross vector b is equal to 25, find dot product of vector a and vector v. Now, again with the solution, we will first write down the given information. We are given that magnitude of vector a is 5, magnitude of vector v is 30, and magnitude of vector a cross vector v is 25. Vector a cross vector v is equal to magnitude of vector a into magnitude of vector b into sin theta, we are given that magnitude of vector A cross vector B is 25, magnitude of vector A is 5 and magnitude of vector B is 30. Now this implies sin theta is equal to 25 divided by 65 and this is equal to 5 by 30. So sin theta is equal to 5 by 30. Now we will find cos theta, cos theta is equal to square root of 1 minus sin square theta and this is equal to square root of 1 minus 25 by 169. This is equal to square root of 144 divided by 169 and this is equal to 12 by 13. Now we will find dot product of vector A dot vector B. Now this is equal to magnitude of vector A into magnitude of vector B into cos theta. The magnitude of vector A is 5, magnitude of vector B is 30 and cos theta is equal to 12 by 13. So this is equal to 60. So dot product of vector A and vector B is equal to 60. This is our required answer. So this one needs the session by antique care.