 Good morning friends, I am Purva and today we will discuss the following question. If vector A is equal to i cap plus j cap plus k cap, vector B is equal to 2 i cap minus j cap plus 3 k cap and vector C is equal to i cap minus 2 j cap plus k cap, find a unit vector parallel to the vector, 2 vector A minus vector B plus 3 vector C. Let us now begin with the solution. Now we are given vector A is equal to i cap plus j cap plus k cap, vector B is equal to 2 i cap minus j cap plus 3 k cap and vector C is equal to i cap minus 2 j cap plus k cap and we have to find a unit vector parallel to 2 vector A minus vector B plus 3 vector C. So first we will find what is 2 vector A minus vector B plus 3 vector C. So we have 2 vector A minus vector B plus 3 vector C is equal to 2 into, now vector A is equal to i cap plus j cap plus k cap minus vector B is equal to 2 i cap minus j cap plus 3 k cap plus 3 into vector C is i cap minus 2 j cap plus k cap. Now we can write this as this is equal to 2 minus 2 plus 3 i cap plus 2 plus 1 minus 6 j cap plus 2 minus 3 plus 3 k cap and we get this implies 2 vector A minus vector B plus 3 vector C is equal to 3 i cap minus 3 j cap plus 2 k cap. Now a unit vector parallel to the vector 2 vector A minus vector B plus 3 vector C is given by this is equal to 2 vector A minus vector B plus 3 vector C upon mod of 2 vector A minus vector B plus 3 vector C. Since we know that a unit vector in the direction of vector A is given by n cap is equal to vector A upon mod of vector A. This is equal to now 2 vector A minus vector B plus 3 vector C is equal to 3 i cap minus 3 j cap plus 2 k cap upon mod of this vector is given by under root of 3 square plus minus 3 square plus 2 square and this is equal to 3 i cap minus 3 j cap plus 2 k cap upon under root of now 3 square is equal to 9. So we have 9 plus minus 3 square is also equal to 9. So we get 9 plus 2 square is 4. So we get 4. This is equal to 3 i cap minus 3 j cap plus 2 k cap upon under root 22. We can also write this as this is equal to 3 upon root 22 i cap minus 3 upon root 22 j cap plus 2 upon root 22 k cap. Hence a unit vector parallel to the vector 2 vector A minus vector B plus 3 vector C is 3 upon root 22 i cap minus 3 upon root 22 j cap plus 2 upon root 22 k cap. This is our answer. Hope you have understood the solution. Bye and take care.