 Good morning friends. I am Purva and today I will help you with the following question. Show that the vector i cap plus j cap plus k cap is equally inclined to the axis O x, O y and O z. Let us now begin with the solution. Now we denote i cap plus j cap plus k cap by vector a. So let vector a is equal to i cap plus j cap plus k cap. Then we have mod of vector a is equal to under root of 1 square plus 1 square plus 1 square and this is equal to under root of 1 plus 1 plus 1 which is equal to root 3. So we have got mod of vector a is equal to root 3. Now the unit vector in the direction of vector a that is n cap is given by vector a upon mod of vector a and we have this is equal to now vector a is equal to i cap plus j cap plus k cap upon mod of vector a is equal to root 3. So we have root 3 and this is further equal to 1 upon root 3 i cap plus 1 upon root 3 j cap plus 1 upon root 3 k cap. So we have got n cap is equal to 1 upon root 3 i cap plus 1 upon root 3 j cap plus 1 upon root 3 k cap. Now the direction cosines of this vector are 1 upon root 3 comma 1 upon root 3 comma 1 upon root 3. Now the direction cosines are given by cos alpha cos beta cos gamma. So we have that is cos alpha is equal to 1 upon root 3 cos beta is equal to 1 upon root 3 and cos gamma is equal to 1 upon root 3. Now we can clearly see that cos alpha is equal to cos beta is equal to cos gamma. So we have this implies cos alpha is equal to cos beta is equal to cos gamma and this implies alpha is equal to beta is equal to gamma. Now since all the three angles have come out to be equal. So we have this implies the vector is equally inclined. Thus we write our answer as the vector i cap plus j cap plus k cap is equally inclined to the axis o x o y and o z. Hope you have understood the solution. Bye and take care.