Question

If the z-axis is vertical and r̂, θ̂^ and φ̂ are unit vectors in spherical coordinates (standard symbols)


(a) r̂ is always horizontal

(b) θ̂^ is always horizontal

(c) φ̂ is always horizontal

(d) θ̂^ can be vertical

[Note:- This question have one or more than one correct choice(s) out of the four given choices. Any number of options may be correct.]

Answer 1

Here, (c) and (d) option are correct since ,

$\theta$^ is the angle made by the vector with respect to z-axis. When

$\theta$^=0 or 180^°, then it is vertical

Also, $\phi$ ^ is in xy-plane, therefore, it lies in the vertical direction as compared to z-axis.