The position vector of a moving particle at t | vedclass

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(D) The displacement $\Delta r$ is given by the difference between the final position vector $r_f$ and the initial position vector $r_i$.Given $r(t) =

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None of these

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(D) The displacement $\Delta r$ is given by the difference between the final position vector $r_f$ and the initial position vector $r_i$.Given $r(t) = 3 \hat{i} + 4t \hat{j} - t \hat{k}$.At $t = 1 \ s$,$r_1 = 3 \hat{i} + 4(1) \hat{j} - (1) \hat{k} = 3 \hat{i} + 4 \hat{j} - \hat{k}$.At $t = 3 \ s$,$r_3 = 3 \hat{i} + 4(3) \hat{j} - (3) \hat{k} = 3 \hat{i} + 12 \hat{j} - 3 \hat{k}$.Displacement $\Delta r = r_3 - r_1 = (3 \hat{i} + 12 \hat{j} - 3 \hat{k}) - (3 \hat{i} + 4 \hat{j} - \hat{k})$.$\Delta r = (3-3) \hat{i} + (12-4) \hat{j} + (-3 - (-1)) \hat{k} = 0 \hat{i} + 8 \hat{j} - 2 \hat{k}$.Since $8 \hat{j} - 2 \hat{k}$ is not among the options $A, B,$ or $C$,the correct choice is $D$.

The position vector of a moving particle at time $t$ is $r = 3 \hat{i} + 4t \hat{j} - t \hat{k}$. Its displacement during the time interval $t = 1 \ s$ to $t = 3 \ s$ is

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