Question

If a line makes angles 90∘,135∘, 45∘ with the x, y and z-axes respectively, find its direction cosines.

Answer 1

Hey.

Here is the answer.

The cosine of the angles made by the directed line, passing through the orgin with the x, y and z axes are called direction cosines.

Given that α=90∘ ,β =135∘ and γ=45∘

The direction cosines are

cosα=cos90∘=0

cosβ=cos135∘=cos(180∘−45∘)= - 1/√2

cosγ=cos45∘=1

Hence the direction cosines are (0, -1/√2 , 1 )

Thanks.

Answer 2

Hey !!

Since the line makes angle 90° , 135° , 45° with the x , y and z axis respectively.

                                       then α = 90° , β = 135° , γ = 45°

l = cos 90° = 0 , m = cos 135° = cos (180 - 45)° = -cos 45°

              =  - 1/√2 and n = cos 45° = 1/√2

Thus, direction cosines of the line are 0 , -1/√2 and 1/√2

GOOD LUCK !!