# 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

Question

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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1 year 2021-09-01T12:14:28+00:00 1 Answers 6 views 0

$$\hat{i} + 3.0 \hat{j} – 10 \hat{k}$$

Explanation:

The final position is given by $$\vec{r} = 3.0 \hat{i} – 4.0 \hat{k}$$

The displacement is

$$\nabla\vec{r} = 2.0\hat{i} – 3.0 \hat{j} + 6\hat{k}$$

The initial position is given by

$$\vec{r} – \vec{p} = \nabla\vec{r}$$

$$\vec{p} = \vec{r} – \nabla\vec{r}$$

$$\vec{p} = 3\hat{i} – 4.0 \hat{k} – (2\hat{i} – 3\hat{j} + 6\hat{k})$$

$$\vec{p} = \hat{i} + 3.0 \hat{j} – 10 \hat{k}$$