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image_path = '/mnt/data/1733549755130618cdum8.jpg' img = Image.open(image_path) img.show()I have displayed the image you uploaded. Let me process it and extract any relevant mathematical content. pytesseract

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text = pytesseract.image_to_string(img)

Output the extracted text

textThe image contains the following mathematical problem:

"Find a unit vector in the direction of $\mathbf{r} = -10\mathbf{i} + 14\mathbf{j}$. Express your answer in terms of $\mathbf{i}$ and $\mathbf{j}$. Give your answer in exact form."

Solution:

A unit vector is a vector with a magnitude of 1, in the same direction as the given vector. To find the unit vector in the direction of $\mathbf{r} = -10\mathbf{i} + 14\mathbf{j}$, follow these steps:

1. Calculate the magnitude of $\mathbf{r}$:

   $|\mathbf{r}| = \sqrt{(-10)^2 + 14^2}$ $|\mathbf{r}| = \sqrt{100 + 196} = \sqrt{296}$

2. Divide the vector $\mathbf{r}$ by its magnitude:

   The unit vector $\mathbf{u}$ in the direction of $\mathbf{r}$ is:

   $\mathbf{u} = \frac{\mathbf{r}}{|\mathbf{r}|} = \frac{-10\mathbf{i} + 14\mathbf{j}}{\sqrt{296}}$

Thus, the unit vector is:

$\mathbf{u} = \frac{-10}{\sqrt{296}} \mathbf{i} + \frac{14}{\sqrt{296}} \mathbf{j}$

This is the exact form of the unit vector in terms of $\mathbf{i}$ and $\mathbf{j}$.

Would you like more details on the steps, or do you have any other questions?

Related questions:

1. How do you calculate the magnitude of a 2D vector?
2. What is the difference between a unit vector and a direction vector?
3. How do you find a unit vector in 3D space?
4. What are some practical applications of unit vectors in physics?
5. How does normalizing a vector relate to its magnitude?

Tip:

When calculating the unit vector, it's always important to first find the magnitude and then divide each component of the vector by this magnitude. This keeps the direction the same but ensures the vector's length becomes 1.