Answer :

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


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