Test Index

CBSE Class 12 Math 2024 All Sets Solved Paper

© examsnet.com
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:
Solution:  
Formula to be used: l2+m2+n2=1l^2 + m^2 + n^2 = 1 where l, m and n are direction cosines (cos⁡α,cos⁡β,cos⁡γ)(\cos α, \cos β, \cos γ) of a given line.
Given
l=cos⁡30∘=  32⇒l2=  34l = \cos 30^{\circ} = \; \frac{\sqrt{3}}{2} \Rightarrow l^2 = \; \frac{3}{4}
m=cos⁡120∘=  12⇒m2=  14m = \cos 120^{\circ} = \; \frac{1}{2} \Rightarrow m^2 = \; \frac{1}{4}
l2+m2+n2=1l^2 + m^2 + n^2 = 1
⇒  34+  14+cos⁡2γ=1\Rightarrow \; \frac{3}{4} + \; \frac{1}{4} + \cos^2 γ = 1
⇒1+cos⁡2γ=1\Rightarrow 1+ \cos^2 γ = 1
⇒cos⁡2γ=0\Rightarrow \cos^2 γ = 0
⇒cos⁡γ=0\Rightarrow \cos γ = 0
⇒γ=90∘\Rightarrow γ = 90^{\circ}
© examsnet.com
Go to Question:
Prev Question
Next Question