Question

A positron undergoes a displacement LaTeX: \\abla\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?

Answer 1

`\hat{i} + 3.0 \hat{j} - 10 \hat{k}`

Step-by-step explanation:

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

The displacement is

`\\abla\vec{r} = 2.0\hat{i} - 3.0 \hat{j} + 6\hat{k}`

The initial position is given by

`\vec{r} - \vec{p} = \\abla\vec{r}`

`\vec{p} = \vec{r} - \\abla\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}`