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

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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