combinations-of-planes

Intersection of planes

How do we find the line of intersection of two planes?

• Two planes will either be parallel or they will intersect along a line

  • Consider the point where a wall meets a floor or a ceiling

  • You will need to find the equation of the line of intersection

• If you have the Cartesian forms of the two planes then the equation of the line of intersection can be found by solving the two equations simultaneously

  • As the solution is a vector equation of a line rather than a unique point you will see below how the equation of the line can be found by part solving the equations

  • For example:

    • (1)

    • (2)

• STEP 1: Choose one variable and substitute this variable for λ in both equations

  • For example, letting x = λ gives:

    • (1)

    • (2)

• STEP 2: Rearrange the two equations to bring λ to one side

  • Equations (1) and (2) become

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