 Hi friends, I am Prudhva and today we will discuss the following question show that the direction cosines of a vector equally inclined to the axis O x, O y and O z are 1 upon root 3 comma 1 upon root 3 comma 1 upon root 3. Let us now begin with the solution. Now since the vector makes equal angles, therefore we have alpha is equal to beta is equal to gamma. Now we know that cos square alpha plus cos square beta plus cos square gamma is equal to 1, this implies cos square alpha plus cos square alpha plus cos square alpha is equal to 1. Since we have alpha is equal to beta is equal to gamma, this implies 3 cos square alpha is equal to 1 which further implies cos square alpha is equal to 1 upon 3 and this implies cos alpha is equal to 1 upon root 3. Now again we have cos square alpha plus cos square beta plus cos square gamma is equal to 1 and this implies cos square beta plus cos square beta plus cos square beta is equal to 1. Again since we know that alpha is equal to beta is equal to gamma, this implies 3 cos square beta is equal to 1 which implies cos square beta is equal to 1 upon 3 and this further implies cos beta is equal to 1 upon root 3. Similarly we will get cos gamma is equal to 1 upon root 3. Hence we have proved that the direction cosines that is cos alpha cos beta and cos gamma are 1 upon root 3, 1 upon root 3, 1 upon root 3. This is our answer. Hope you have understood the solution. Bye and take care.