 Good morning friends. I am Purva and today we will discuss the following question. For given vectors vector A is equal to 2i cap minus j cap plus 2k cap and vector B is equal to minus i cap plus j cap minus k cap. Find the unit vector in the direction of the vector vector A plus vector B. Let us now begin with the solution. Now we are given vector A is equal to 2i cap minus j cap plus 2k cap and vector B is equal to minus i cap plus j cap minus k cap. Therefore we have vector A plus vector B is equal to 2i cap minus j cap plus 2k cap plus minus i cap plus j cap minus k cap. And we have this is equal to 2 minus 1 i cap plus minus 1 plus 1 j cap plus 2 minus 1 k cap. This is equal to 1 i cap plus 0 j cap plus 1 k cap. And we can write this as vector A plus vector B is equal to i cap plus k cap. Now to find the unit vector in the direction of vector A plus vector B we have to find mod of vector A plus vector B. So mod of vector A plus vector B is equal to mod of i cap plus k cap and this is equal to under root of 1 square plus 1 square which is equal to under root of 1 plus 1 and this is equal to root 2. Therefore we have got mod of vector A plus vector B is equal to root 2. Now let the unit vector in the direction of vector A plus vector B is given by n cap. So we have n cap is equal to vector A plus vector B upon mod of vector A plus vector B. This is equal to now vector A plus vector B is equal to i cap plus k cap upon mod of vector A plus vector B is equal to root 2. So we get n cap is equal to 1 upon root 2 i cap plus 1 upon root 2 k cap. Hence the unit vector in the direction of vector A plus vector B is 1 upon root 2 i cap plus 1 upon root 2 k cap. This is our answer. Hope you have understood the solution. Bye and take care.