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A positron undergoes a displacement LaTeX: \nabla\vec{r}=\:2.0\hat i - 3.0 \hat j + 6.0 \hat k,∇ r → = 2.0 i ^ − 3.0 j ^ + 6.0 k ^ , ending with the position vector LaTeX: \vec{r}=3.0 \hat i - 4.0 \hat k,r → = 3.0 i ^ − 4.0 k ^ , in meters. What was the positron’s initial position vector?

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Answer:

[tex]\hat{i} + 3.0 \hat{j} - 10 \hat{k}[/tex]

Explanation:

The final position is given by [tex]\vec{r} = 3.0 \hat{i} - 4.0 \hat{k}[/tex]

The displacement is

[tex]\nabla\vec{r} = 2.0\hat{i} - 3.0 \hat{j} + 6\hat{k}[/tex]

The initial position is given by

[tex]\vec{r} - \vec{p} = \nabla\vec{r}[/tex]

[tex]\vec{p} = \vec{r} - \nabla\vec{r}[/tex]

[tex]\vec{p} = 3\hat{i} - 4.0 \hat{k} - (2\hat{i} - 3\hat{j} + 6\hat{k})[/tex]

[tex]\vec{p} = \hat{i} + 3.0 \hat{j} - 10 \hat{k}[/tex]

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