If a unit vector 
makes an angle 
with 
with
and an acute angle θ with 
, then find the value of θ.
Given the unit vector makes,
• an angle of 
with x-axis
• an angle of 
with y-axis
• an angle of θ with z-axis
• θ is acute angle
Let the unit vector 
be: 
As given it is a unit vector,
Therefore 
= 1
As the angle between in 
and x-axis is 
, the scalar product of the vectors can be performed.
The scalar product of the two vectors is given by
[as both the vectors are of magnitude 1].
As the angle between in 
and y-axis is 
, the scalar product of the vectors can be performed.
Similarly the angle between in 
and y-axis is θ , the scalar product of the vectors can be performed.
The magnitude of a vector x
+ y
+ z 
is given by 
.
Now consider the magnitude of the vector 
1 
1 
[Squaring on both sides]
1 = 
cos2θ 
cos2θ = 
cos θ = 
cosθ = 
As given in the question θ is acute angle, so θ belongs to 1st quadrant and is positive.
Therefore