Question

A line in the third dimensional space makes an angle o (0<o<pi/2) with both x and y axes. then set all the values of is the interval:​

Answer 1

Three Dimensional Geometry

Direction Cosines and Direction Ratios

A line in the 3-dimensional...

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Asked on October 15, 2019 by

Gungun Pintu

A line in the 3-dimensional space makes an angle θ(0<θ≤

2

π

) with both the x and y axes, then the set of all values of θ is the interval :

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VIDEO EXPLANATION

ANSWER

Sum of square of direction cosines is 1.

Lets assume α is the angle with x, β with y and γ with z.

α,β,γ∈[0,

2

π

]

Now,

cos

2

α+cos

2

β+cos

2

γ=1

But it is given that, α=β=θ

∴cos

2

θ+cos

2

θ+cos

2

γ=1

⇒2cos

2

θ=1−cos

2

γ

⇒=cos

2

θ=

2

sin

2

γ

⇒cosθ=

2

sinγ

As γ∈[0,

2

π

], then θ∈[

4

π

,

2