Question

Find d.c.s of a line whose direction angles with X-axis Y-axis are 45° and 60°​

Answer 1

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Answer 2

Answer:

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Step-by-step explanation:

If α,β,γ are the angles made by a line with the positive direction of x-axis,y-axis and z-axis then cosα,cosβ,cosγ are called the direction cosines of the line.

Also cos

2

α+cos

2

β+cos

2

γ=1

Given α=45

∘

,β=60

∘

⇒cos

2

45

∘

+cos

2

60

∘

+cos

2

γ=1

⇒(

2

1

)

2

+(

2

1

)

2

+cos

2

γ=1

⇒

2

1

+

4

1

+cos

2

γ=1

⇒cos

2

γ=1−

2

1

−

4

1

⇒cos

2

γ=1−

4

3

⇒cos

2

γ=

4

1

⇒cosγ=

2

1

⇒γ=cos

−1

(

2

1

)

⇒γ=60

∘