Question

how many straight line in space through the origin we equally inclined to the co-ordinate axis?​

Answer 1

Step-by-step explanation:

If α,β,γ are the angles made by the line with x,y, and z-axis, respectively, then

cos

2

α+cos

2

β+cos

2

γ=1

Given, α=β=γ

∴3cos

2

α=1 or, cosα=±

3

1

Possible direction cosines are (±

3

1

,±

3

1

,±

3

1

).

Different sets of d.c

′

s are (

3

1

,

3

1

,

3

1

),(

3

1

,

3

1

,

3

−1

),(

3

1

,

3

−1

,

3

1

)

and (

3

−1

,

3

1

,

3

1

)

Thus, four lines are equally inclined to axes.