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Class 12th Mathematics 2017 Set1 Delhi Board Paper Solution

Question 4

If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.

Answer

Here, α = 90° , β = 60°

Let γ = θº, where 0 ≤ θº ≤ π

Now cos2 α + cos2 β + cos2 γ = 1 

⇒ cos2 90° + cos2 60° + cos2 θº = 1 

⇒ 02 + (½)2 + cos2 θº = 1

cos2 θ = 1- 1/4 = 3/4

cos θ = ± √3 / 2

 θ = π / 6  or  5π / 6

 

 

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