 Hello and welcome to the session. In this session we shall discuss about vector all cross product of two vectors. Vector product of two non-zero vectors, vector A and vector B is given by vector A cross vector B equal to magnitude of vector A into magnitude of vector B sin theta n cap. Where this theta is the angle between vector A and vector B and theta should be greater than equal to zero and less than equal to pi. Also this n cap is the unit vector perpendicular to both vector A and vector B. Such that vector A vector B n cap form right handed system of coordinate axis. If either vector A is equal to zero vector or vector B is equal to zero vector then theta is not defined and in this case vector A cross vector B would be equal to zero vector. And the cross product of two non-zero vectors vector A cross vector B will be a vector. Then vector A cross vector B is equal to zero vector if and only if vector A and vector B are parallel to each other or we can say that vector A and vector B are collinear to each other. If in the formula for cross product of two vectors we have theta is equal to pi by two then vector A cross vector B is equal to magnitude of vector A into magnitude of vector B. If we have i cap j cap k cap are mutually perpendicular unit vectors then i cap cross i cap is equal to j cap cross j cap is equal to k cap cross k cap is equal to zero vector. Then i cap cross j cap is equal to k cap j cap cross k cap is equal to i cap and k cap cross i cap is equal to j cap. In terms of vector product the angle between two vectors vector A and vector B may be given by sin theta equal to magnitude of vector A cross vector B upon magnitude of vector A into magnitude of vector B. And then vector product is not commutative that is vector A cross vector B is equal to minus vector B cross vector A. If we have vector A and vector B are the adjacent sides of a triangle then the area of this triangle is given by half multiplied by magnitude of vector A cross vector B. And if vector A and vector B are the adjacent sides of a parallelogram then its area that is area of the parallelogram would be given by magnitude of vector A cross vector B. Now we have properties of vector product. The first property of vector product is distributivity of vector product over addition. According to this we have if vector A vector B vector C are any three vectors given to us then vector A cross vector B plus vector C is equal to vector A cross vector B plus vector A cross vector C. Then the next property is if A B C are any three vectors and lambda is any scalar then we have lambda multiplied by vector A cross vector B is equal to lambda into vector A cross vector B is equal to vector A cross lambda into vector B. The next we have if we have two vectors vector A and vector B given in component form that is vector A is equal to A1 i cap plus A2 j cap plus A3 k cap and vector B is equal to B1 i cap plus B2 j cap plus B3 k cap. Then cross product of vector A and vector B is given by determinant i cap j cap k cap A1 A2 A3 B1 B2 B3. Let's consider vector A equal to i cap minus 7 j cap plus 7 k cap and vector B equal to 3 i cap minus 2 j cap plus 2 k cap. Then the cross product of these two vectors is given by determinant i cap j cap k cap then A1 that is 1 A2 that is minus 7 A3 that is 7 then B1 that is 3 B2 minus 2 B3 is 2. This becomes equal to i cap into minus 14 plus 14 minus j cap into 2 minus 21 plus k cap into minus 2 plus 21 so this becomes equal to 19 j cap plus 19 k cap that is vector A cross vector B is equal to 19 j cap plus 19 k cap. This is how we find the cross product of two vectors or you can say vector product of two vectors. This completes our session. Hope you have understood the vector product of two vectors.