3D Geometry
Lines in 3D
Grade 12
Question:
<p>Equation of the line through the point (1, 1, 1) and intersecting the lines \(2x - y - z - 2 = 0 = x + y + z - 1\) and \(x - y - z - 3 = 0 = 2x + 4y - z - 4\)</p>
<p>(a) \(x - 1 = 0, 7x + 17y - 3z - 134 = 0\)</p>
<p>(b) \(x - 1 = 0, 9x + 15y - 5z - 19 = 0\)</p>
<p>(c) \(x - 1 = 0, \frac{y - 1}{1} = \frac{z - 1}{3}\)</p>
<p>(d) \(x - 2y + 2z - 1 = 0, 9x + 15y - 5z - 19 = 0\)</p>
Step-by-Step Solution
Key Concept: Find a line through a given point that intersects two lines formed by pairs of planes.
The line passes through (1, 1, 1) and must intersect both given pairs of lines. Setting up the system and solving yields the equation \(x - 1 = 0, 9x + 15y - 5z - 19 = 0\).
Correct Answer: B