The displacement of a particle from a point h | vedclass

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Question

(B) The displacement vector $\vec{d}$ is the difference between the final position vector $\vec{r}_f$ and the initial position vector $\vec{r}_i$.Give

Vedclass · Accepted Answer

$3 \sqrt{2}$

Vedclass · Answer

(B) The displacement vector $\vec{d}$ is the difference between the final position vector $\vec{r}_f$ and the initial position vector $\vec{r}_i$.Given $\vec{r}_i = 2 \hat{i} + 4 \hat{j}$ and $\vec{r}_f = 5 \hat{i} + 1 \hat{j}$.$\vec{d} = \vec{r}_f - \vec{r}_i = (5 \hat{i} + 1 \hat{j}) - (2 \hat{i} + 4 \hat{j})$.$\vec{d} = (5 - 2) \hat{i} + (1 - 4) \hat{j} = 3 \hat{i} - 3 \hat{j}$.The magnitude of the displacement is $|\vec{d}| = \sqrt{(3)^2 + (-3)^2}$.$|\vec{d}| = \sqrt{9 + 9} = \sqrt{18} = 3 \sqrt{2}$ units.Hence,option $B$ is the correct answer.

The displacement of a particle from a point having position vector $2 \hat{i} + 4 \hat{j}$ to another point having position vector $5 \hat{i} + 1 \hat{j}$ is ........ units.

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