<p>Find the point where the line $$\frac{x - 2}{3} = \frac{y - 1}{4} = \frac{z - 6}{5}$$ intersects the plane <i>x</i> + <i>y</i> - 2<i>z</i> = 3.</p>
Step-by-Step Solution
Key Concept: Substitute parametric equations of the line into the plane equation to find the parameter value, then find the coordinates.
Solution: Parametric equations: x = 2 + 3λ, y = 1 + 4λ, z = 6 + 5λ Substituting in the plane equation: 2 + 3λ + 1 + 4λ - 2(6 + 5λ) = 3 3 + 7λ - 12 - 10λ = 3 -3λ = 12 λ = -4 Therefore: x = 2 - 12 = -10, y = 1 - 16 = -15, z = 6 - 20 = -14 ∴ Point is (-10, -15, -14)
Correct Answer: B