In spherical polar coordinates (γ, θ, α), θ denotes the polar angle around z-axis and α denotes the azimuthal angle raised from x-axis. Then the y-component of P⃗ is given by
Psinθsinα
Psinθcosα
Pcosθsinα
Pcosθcosα
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CDS-1 – 2019
$P_x = P \sin\theta \cos\alpha$
$P_y = P \sin\theta \sin\alpha$
$P_z = P \cos\theta$
The question asks for the y-component of P⃗. According to the standard conversion from spherical to Cartesian coordinates, the y-component is $P\sin\theta\sin\alpha$.
– γ (or P) is the magnitude.
– θ is the angle from the z-axis (polar angle).
– α is the angle from the x-axis in the xy-plane (azimuthal angle).
– The projection onto the xy-plane has length $P\sin\theta$.
– This projection is resolved into x and y components using the azimuthal angle α.