 Hello and welcome to this session. In this session we discuss the following question which says write a vector of the magnitude 15 units in the direction of vector i cap minus 2j cap plus 2k cap. We know that a unit vector in the direction of vector a is given by a cap and this is equal to vector a upon magnitude of vector a. This is the key idea that we use for this question. Let's now proceed with the solution. We suppose let vector a be equal to i cap minus 2j cap plus 2k cap. Now the magnitude of vector a would be equal to the square root of the sum of the squares of the scalar components of vector a. So this would be equal to square root of 1 square plus minus 2j square plus 2 square which means that magnitude of vector a is equal to square root of 1 plus 4 plus 4 which is equal to square root 9 and this is equal to 3. Thus we have magnitude of vector a is equal to 3. Now the unit vector in the direction of vector a is given by a cap and this is equal to vector a which is i cap minus 2j cap plus 2k cap upon magnitude of vector a which is 3. That is we have a cap is equal to 1 by 3 i cap minus 2 by 3j cap plus 2 by 3k cap and we are supposed to find the vector of magnitude 15 units in the direction of the given vector which we have taken as vector a. So vector having magnitude equal to 15 is given by 15 into a cap which would be equal to 15 into 1 by 3 i cap minus 2 by 3j cap plus 2 by 3k cap the whole. So this is equal to 5 i cap minus 10j cap this could also be written as 5 into i cap minus 2j cap plus 2k cap the whole. Thus we can say vector of magnitude 15 units direction of 2j cap plus 2k cap given by 5 into plus 2j cap plus 2k cap the whole. So we say 5 into i cap minus 2j cap plus 2k cap the whole is our final answer. This completes the session but we have understood the solution of this question.