 Good morning friends. I am Purva and today we will discuss the following question. Choose the correct answer and the question is if theta is the angle between any two vectors vector a and vector b then mod of vector a dot vector b is equal to mod of vector a cross vector b when theta is equal to a0 b pi by 4 c pi by 2 d pi. Let us now begin with the solution. Now since theta is the angle between vector a and vector b therefore we have cos theta is equal to vector a dot vector b upon mod of vector a into mod of vector b. Now this implies vector a dot vector b is equal to mod of vector a into mod of vector b into cos theta. Taking mod we get mod of vector a dot vector b is equal to mod of vector a into mod of vector b into cos theta. Now again since theta is the angle between vector a and vector b therefore we have vector a cross vector b is equal to mod of vector a into mod of vector b into sin theta into n cap where n cap is a unit vector perpendicular to the plane containing vector a and vector b. Taking mod we get mod of vector a cross vector b is equal to mod of vector a into mod of vector b into sin theta into mod of n cap. Now since n cap is a unit vector therefore we have mod of n cap is equal to 1 so we get this implies mod of vector a cross vector b is equal to mod of vector a into mod of vector b into sin theta. Now we are given that mod of vector a dot vector b is equal to mod of vector a cross vector b. This implies now mod of vector a dot vector b is equal to mod of vector a into mod of vector b into cos theta and this is equal to now mod of vector a cross vector b is equal to mod of vector a into mod of vector b into sin theta. This implies cos theta is equal to sin theta and this implies cos theta is equal to cos 90 minus theta. This implies theta is equal to pi by 2 minus theta which implies 2 theta is equal to pi by 2 and this implies theta is equal to pi by 4. So we have got the value of theta as pi by 4 and this is same as option b. So we write our answer as b. Hope you have understood the solution. Bye and take care.