# Practice Problems¶

### Lecture 21¶

Answer each number in a separate cell

Rename the notebook with your lastName and the lecture

ex. CychB_21



Turn this notebook into TritonEd by the end of class

# 1. Cartesian coordinates and polar coordinates¶

• Write lambda functions to replace dir2cart() and cart2dir(). Call them dir_cart and cart_dir
• You measured a bedding plane with an azimuth of 40 and a plunge of 62. Use your function dir_cart() to convert the coordinates to cartesian coordinates.
• Use your function cart_dir() to convert the cartesian coordinates back to polar coordinates
• test your functions by calling the dir2cart() and cart2dir() funtions in the lecture.
• modify cart2dir() to round to the nearest decimal

# 2. Unit vectors¶

• What is the sum of the two vectors Az1=245, Pl1=22 and Az2=10, Pl2=60?
• What is the difference between these vectors?
• What is angle between the two vectors?
• What is pole to the two vectors?
• Make an equal angle diagram
• plot the two vectors as green triangles
• plot the pole to the plane as a blue star

## 3. Vectors with length¶

• Modify the function dir2cart() from the lecture to include vector length $R$. Call it vec2cart().
• Apply your new function to evaluate the cartesian coordinates of the vector with Azimuth=12, Plunge=42, R=8
• Modify the function cart2dir() to return the full vector (Azimuth, Plunge and $R$) from the cartesian coordinates. Call this one cart2vec().
• Verify that your function works, by feeding the output of dir2cart() back into cart2dir() to make sure you get back what you started with.
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