 Good morning friends I am Purva and today we will discuss the following question. Find the direction cosines of the vector i cap plus 2 j cap plus 3 k cap. Let us now begin with the solution. Now let us denote i cap plus 2 j cap plus 3 k cap by vector a. So let vector a is equal to i cap plus 2 j cap plus 3 k cap. Now mod of vector a is given by mod of i cap plus 2 j cap plus 3 k cap and this is equal to under root of 1 square plus 2 square plus 3 square and this is equal to under root of 1 square is equal to 1. So we have 1 plus 2 square is equal to 4 plus 3 square is equal to 9 and this is equal to under root 14. So we have got mod of vector a is equal to root 14. Now let n cap be the unit vector in the direction of vector a that is i cap plus 2 j cap plus 3 k cap. So we have n cap is equal to vector a upon mod of vector a. This is equal to now vector a is equal to i cap plus 2 j cap plus 3 k cap upon mod of vector a is equal to root 14. So we have n cap is equal to 1 upon root 14 i cap plus 2 upon root 14 j cap plus 3 upon root 14 k cap. Now the direction cosines of vector a will be the coefficients of i cap, j cap and k cap of its unit vector that is n cap. Therefore the direction cosines of vector a which is equal to i cap plus 2 j cap plus 3 k cap are 1 upon root 14 comma 2 upon root 14 comma 3 upon root 14. So this is our answer. Hope you have understood the solution. Bye and take care.