Question

The coordinates of the point where the line through the points \( A(3, 4, 1) \) and \( B(5, 1, 6) \) crosses the \( XY \)-plane are

• A. \( \left( \frac{13}{5}, 0, 0 \right) \)
• B. \( \left( \frac{13}{5}, 5, 0 \right) \)
• C. \( \left( \frac{13}{5}, 23, 0 \right) \)
• D. \( \left( \frac{13}{5}, 0, 5 \right) \)

Hint:

To find the intersection of a line with the \( XY \)-plane, set \( z = 0 \) and solve for the coordinates.

Answer 1

The Correct Option is A

Step 1: Use the section formula.
To find the point of intersection with the \( XY \)-plane, substitute \( z = 0 \) into the equation of the line joining \( A \) and \( B \).
Step 2: Conclusion.
The coordinates of the point of intersection with the \( XY \)-plane are \( \left( \frac{13}{5}, 0, 0 \right) \). Final Answer: \[ \boxed{\left( \frac{13}{5}, 0, 0 \right)} \]