Find the equation of a plane that contains two given lines by finding their intersection point and taking the cross product of their direction vectors.

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Equation of a Plane Containing Two Intersecting Lines

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Find an equation of the plane containing the lines $L_1$ and $L_2$: \[ L_1: x = -y = z \] \[ L_2: \frac{x-3}{2} = y = z - 2 \]

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What you need first

Extracting direction vectors from symmetric equations of lines
Converting symmetric equations to parametric equations
Finding the intersection of two lines in 3D space
Computing the cross product of two 3D vectors
Writing the equation of a plane given a point and a normal vector

What this problem tests

Tests the student's ability to extract geometric information from symmetric equations, compute a cross product to find a normal vector, and assemble the equation of a plane.

This is a standard problem in multivariable calculus and linear algebra courses, testing the ability to relate lines and planes in three-dimensional space.

Equation of a Plane Containing Two Intersecting Lines

What you need first

What this problem tests

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