Question:medium
Equation of the line through the point (2, 3, 1) and parallel to the line of intersection of the planes \( x - 2y - z + 5 = 0 \) and \( x + y + 3z = 6 \) is:
Equation of the line through the point (2, 3, 1) and parallel to the line of intersection of the planes \( x - 2y - z + 5 = 0 \) and \( x + y + 3z = 6 \) is:
Show Hint
The line of intersection of two planes is always parallel to $\vec{n_1} \times \vec{n_2}$. This vector represents the direction where both planes are "advancing" together.
Updated On: May 6, 2026
- \( \frac{x - 2}{-5} = \frac{y - 3}{-4} = \frac{z - 1}{3} \)
- \( \frac{x - 2}{5} = \frac{y - 3}{-4} = \frac{z - 1}{3} \)
- \( \frac{x - 2}{5} = \frac{y - 3}{4} = \frac{z - 1}{3} \)
- \( \frac{x - 2}{4} = \frac{y - 3}{3} = \frac{z - 1}{2} \)
- \( \frac{x - 2}{-4} = \frac{y - 3}{-3} = \frac{z - 1}{2} \)
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The Correct Option is A
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