Two particles P_1 and P_2 are moving with vel | vedclass

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(C) The relative velocity of particle $P_1$ with respect to $P_2$ is defined as $\vec{v}_{12} = \vec{v}_1 - \vec{v}_2$.Using the triangle inequality f

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$v_{12}$ cannot be greater than $v_1 + v_2$

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(C) The relative velocity of particle $P_1$ with respect to $P_2$ is defined as $\vec{v}_{12} = \vec{v}_1 - \vec{v}_2$.Using the triangle inequality for vectors,the magnitude of the relative velocity is given by $|\vec{v}_{12}| = |\vec{v}_1 + (-\vec{v}_2)|$.According to the triangle inequality,$|\vec{a} + \vec{b}| \leq |\vec{a}| + |\vec{b}|$.Substituting $\vec{a} = \vec{v}_1$ and $\vec{b} = -\vec{v}_2$,we get $|\vec{v}_{12}| \leq |\vec{v}_1| + |-\vec{v}_2|$.Since $|-\vec{v}_2| = |\vec{v}_2|$,this simplifies to $|\vec{v}_{12}| \leq v_1 + v_2$.Therefore,the relative velocity $v_{12}$ cannot be greater than the sum of the magnitudes of the individual velocities $v_1 + v_2$.

Two particles $P_1$ and $P_2$ are moving with velocities $v_1$ and $v_2$ respectively. Which of the following statements about their relative velocity $v_{12}$ is true?

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