Question

Find the direction cosines of line which makes a equalangles with the coordinate axes​

Answer 1

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

Hence the required direction cosine are

±1/√3 , ±1/√3 , ±1/√3 Ans







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