Math miscellaneousHard
Question
A line AB in three-dimensional space makes angles 45o and 120o with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle θ with the positive z-axis, then θ equals
Options
A.45o
B.60o
C.75o
D.30o
Solution
l = cos 45o = 
m = cos 120o = -
n = cos θ
where θ is the angle which line makes with positive z-axis.
Now l2 + m2 + n2 = 1
+ cos2 θ = 1
cos2 θ =
⇒ cos θ 
(θ Being acute)
m = cos 120o = -
n = cos θ
where θ is the angle which line makes with positive z-axis.
Now l2 + m2 + n2 = 1
+ cos2 θ = 1cos2 θ =
⇒ cos θ (θ Being acute)Create a free account to view solution
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