Q. 195.0( 1 Vote )
If a unit vector
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
[Squaring on both sides]
cos θ =
As given in the question θ is acute angle, so θ belongs to 1st quadrant and is positive.
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