 Hi and welcome to the session. Let us discuss the following question. Question says, let the vectors a, b, c be given as a1i plus a2j plus a3k, b1i plus b2j plus b3k, c1i plus c2j plus c3k. Then show that a vector cross b vector plus c vector is equal to a vector cross b vector. Let us now start with the solution, how we know a vector is equal to a1i plus a2j plus a3k b vector is equal to b1i plus b2j plus b3k and c vector is equal to c1i plus c2j plus c3k. Now we have to show that a vector cross b vector plus c vector is equal to a vector cross b vector plus a vector cross c vector. First of all let us consider left hand side, now this a vector cross b vector plus c vector. Now we know vector a is equal to a1i plus a2j plus a3k cross vector b plus vector c is equal to b1 plus c1i plus b2 plus c2j plus b3 plus c3k, now cross product of these two vectors is equal to determinant of unit vector i, unit vector j, unit vector k, a1, a2, a3, b1 plus c1, b2 plus c2, b3 plus c3. Now this determinant can be further written as sum of two determinants that is determinant of unit vector i, unit vector j, unit vector k, a1, a2, a3, b1, b2, b3 plus determinant of unit vector i, unit vector j, unit vector k, a1, a2, a3, c1, c2, c3. Here we have used the property of determinants that if each element of a row of a determinant is expressed as a sum of two or more terms then determinant can be expressed as sum of two or more determinants, now clearly we can see this determinant represents the vector product a vector cross b vector and we will write this plus sign as it is, now this determinant represents vector product a vector cross c vector. Now clearly we can see this is the right hand side of the given expression, so we get left hand side is equal to right hand side, so we get a vector cross b vector plus c vector is equal to a vector cross b vector plus a vector cross c vector hence proved. This completes the session hope you understood the solution take care have a nice day.