If a line makes an angle of 30° with the positive direction ...

CBSE Class 12 Math 2024 All Sets Solved Paper

Question : 18 of 20

Marks: +1, -0

If a line makes an angle of 30° with the positive direction of x-axis, 120° with the positive direction of y-axis, then the angle which it makes with the positive direction of z-axis is:

90°
120°
60°
0°

Solution:

Formula to be used:

l^2 + m^2 + n^2 = 1

where l, m and n are direction cosines

(\cos α, \cos β, \cos γ)

of a given line.
Given

l = \cos 30^∘ = \;{√ 3}/{2} ⇒ l^2 = \;{3}/{4}

m = \cos 120^∘ = \;{1}/{2} ⇒ m^2 = \;{1}/{4}

l^2 + m^2 + n^2 = 1

⇒ \;{3}/{4} + \;{1}/{4} + \cos ^2 γ = 1

⇒ 1+ \cos ^2 γ = 1

⇒ \cos ^2 γ = 0

⇒ \cos γ = 0

⇒ γ = 90^∘

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