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Two bodies A and B are moving with velocities `vec(V)_(A) and vec(V)_(B)` making an `'theta'` with each other. Determine the relative velocity of A with respect to B. What will be the relative velocity .
When two bodies are moving in the same direction.

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Let us consider the velocities `vec(V)_(A) and vec(B)` at an angle `theta` between their directions. The relative velocity of A with respect to B, `vec(v) _(AB) = vec(v)_(A) - vec(B)` .
Then , the magnitude and direction of . `vec(V)_(AB)` is given by `v_(AB) = sqrt(v_(A)^(2) + v_(B)^(2) - 2v_(A) v_(B) cos theta)` and tan `beta = (v_(B) sin theta)/(v_(A) - v_(B) cos theta)` (Here `beta` is angle between `vec(v)_(AB) and vec(v)_(B)` ) .
When `theta = 0` , the bodies move along parallel straight lines in the same direction.
We have `v_(AB) = (v_(A) - v_(B))` in the direction of `vec(v)_(A)` . Obviously `v_(AB) = (v_(B) - v_(A))` in the direction of `vec(v)_(B)` .
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