 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that if vector A is equal to the ordered pair minus 4 8, then find 3 by 2 into vector A, also find magnitude of 3 by 2 into vector A. Now let us start with the solution of the given question. Now in this question we are given vector A in component form that is vector A is equal to the ordered pair minus 4 8 and we have to find 3 by 2 into vector A. Here we have to multiply the given vector with scalar 3 by 2. We know that if component form of a vector is given that is we have vector V is equal to the ordered pair xy then its scalar multiplication with the given scalar k is given by k into vector V is equal to k into the ordered pair xy which is equal to the ordered pair kxky that is we multiply each component of the vector with the given scalar k. So here we have scalar k is equal to 3 by 2 so 3 by 2 into vector A is equal to 3 by 2 into the ordered pair minus 4 8 which is equal to the ordered pair 3 by 2 into minus 4 3 by 2 into 8 which is equal to the ordered pair minus 6 12. So 3 by 2 into vector A is given by the ordered pair minus 6 12. Now we shall find its magnitude that is magnitude of 3 by 2 into vector A. Now we know that for any vector V given by the ordered pair xy its magnitude that is magnitude of V will be given by square root of x square plus y square. So here we have 3 by 2 into vector A is equal to the ordered pair minus 6 12 thus its magnitude that is 3 by 2 into A will be equal to square root of minus 6 whole square plus 12 square which is equal to square root of minus 6 whole square is 36 plus 12 square that is 144 which is equal to square root of 180 and this is equal to 6 into square root of 5. Thus its magnitude that is magnitude of 3 by 2 into A is equal to 6 square root of 5 which is the required answer. This completes our session hope you enjoyed this session.