Question

The direction cosines of z-axis are-

1. (0, 0, 0)
2. (1, 0, 0)
3. (0, 0, 1)
4. (0, 1, 0)

Answer: (0, 0, 1)

Solution :-

The direction cosines are values of position vector in 3D plane which made by the position vector by angles $\alpha ,\beta \text{and}\gamma$ with positive direction of $x,y\text{and}z-$ axis respectively.

Then, the direction cosine of any position vector in 3D plane is $\left(cos\alpha ,cos\beta ,cos\gamma \right)\cdot$

If position vector is on the $z-$ axis then angle $\alpha$ made by this vector with positive direction of $x-$ axis is $\frac{\pi }{2}$ and also with positive direction of $y-$ axis is $\frac{\pi }{2}=\beta$ and angle with $z-$ axis is 0 = $\gamma$ .

So, correct answer is option-3 , $\to \left(0,0,1\right)$