Question

Find the direction cosines of a line which makes equal angles with positive co-ordinate axis

Answer 1

1/root 3

If A , B , C are the angle that a line makes with the co-ordinate axes then

We Know from the formula of direction cosine is

Cos²A + cos²B + cos²C = 1 …,,,,,,,,,,,,,,(1 )

Since the line make equal angle with the

co-ordinate axes then

A= B=C= X ( let)……………………….(2)

Hence from equation (1) & (2) we get

cos²x + cos²x + cos²x = 1

3cos²x = 1

Cos²x= 1/3

Cosx = 1/√3

Now cosA = cosB= cosC = +1/√3

Hope it helps u.