When the position vector r⃗=xî+yĵ+zk̂ changes sign as -r⃗, which one of the following vector will not flip under sign change?

Solution

Physics sir · 2 steps

Flip r⃗ and see what each quantity is built from: two flipped vectors crossed together stay put.

1. Parity flip. Under r⃗ → -r⃗, every coordinate changes sign while time stays the same. Any vector made from one power of r⃗ flips with it.

   Quantity	Built from	Under r⃗ → -r⃗
   Velocity	v⃗ = dr⃗/dt	-v⃗, flips
   Linear momentum	p⃗ = mv⃗	-p⃗, flips
   Acceleration	a⃗ = d²r⃗/dt²	-a⃗, flips
   Angular momentum	L⃗ = r⃗ × p⃗	L⃗, does not flip

   L⃗' = (-r⃗) × (-p⃗) = r⃗ × p⃗ = L⃗

2. So. The two minus signs cancel in the cross product, so angular momentum does not flip. The answer is (d).

The idea to keep. A cross product of two vectors that both flip does not flip. Such quantities, like L⃗, torque and B⃗, are called axial vectors or pseudovectors.

Answer from the NTA final answer key. Solution by PrepWiser.