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A person A is moving along east and B is moving along north Then relative velocity of A with respect to B is

A person A is moving along east and B is moving along north. Then relative velocity of A with respect to B is (V_{A}=10\, m/s\, ,\; V_{B}=10\sqrt{3}\, m/s)

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\underset{V_{BA}}{\rightarrow}  =  \underset{V_{B}}{\rightarrow}  - \underset{V_{A}}{\rightarrow}  =10\sqrt{3}\; \hat{j}-10\, \hat{l}

\left | \underset{V_{BA}}{\rightarrow} \right |   =  \sqrt{100+300}=20\, m/s

\tan \theta =\frac{-V_{B}}{V_{A}}=\frac{-10\sqrt{3}}{10}=-\sqrt{3}

\theta =120^{\circ}\; \; from\; \; east

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