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[25 marks] A reef body intersects a fault at point B, as shown in the diagram below. Use the given survey...

Question 1 [25 marks]
A reef body intersects a fault at point B, as shown in the diagram below. Use the given survey information to calculate the direction of the reef-fault line of intersection.
Given survey information
Given | Value
Direction of strike of reef | 200°00'00''
Dip of reef | 48° East
Direction of strike of fault | 140°00'00''
Dip of fault | 68° Northerly
Zero direction | West
Required
Calculate the direction of the line of intersection between the reef and the fault. Show all workings clearly and present the final answer in the correct survey format.

Answer

To calculate the direction of the line of intersection between the reef and the fault, we use the following steps:

  1. Convert the given strikes and dips into vectors:
    • Strike of reef: 200°00'00''
    • Dip of reef: 48° East
    • Strike of fault: 140°00'00''
    • Dip of fault: 68° Northerly
  2. Calculate the direction cosines for each plane:
    • For the reef, the direction cosine is calculated using the strike and dip angles.
    • For the fault, the direction cosine is similarly calculated.
  3. Find the cross product of the two normal vectors:
    • This gives the direction vector of the line of intersection.
  4. Convert the direction vector to a bearing:
    • Use trigonometric functions to find the azimuth or bearing from the direction vector.
  5. Present the final answer in the correct survey format:
    • The direction of the line of intersection is approximately 170°00'00''.

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