Physics I / Lines, Planes, and Geometric Transformations

Practice question · Put in order

Order the steps to find the equation of a plane through 3 points.

Use point-normal form: n $\cdot (r$ − $P_{1}$ ) = 0
Find the normal: $n = v_{1} \times v_{2}$
Compute two vectors in the plane: $v_{1} = P_{2}-P_{1}, v_{2} = P_{3}-P_{1}$
Expand to ax + by + cz = d

Hints

Build two vectors lying in the plane from the three given points.
Their cross product supplies the direction the plane equation needs.

Show the answer

Compute two vectors in the plane: $v_{1} = P_{2}-P_{1}, v_{2} = P_{3}-P_{1}$
Find the normal: $n = v_{1} \times v_{2}$
Use point-normal form: n $\cdot (r$ − $P_{1}$ ) = 0
Expand to ax + by + cz = d

Why

The cross product of two in-plane vectors gives the normal direction.

Read the lesson: Lines, Planes, and Geometric Transformations →

Practise Lines, Planes, and Geometric Transformations

The app has 7 more questions on this lesson, and keeps your place in the course. Physics I is free to start.

Start Physics I free Get it onGoogle Play

More questions on Lines, Planes, and Geometric Transformations