Porisma

A hint to get started

Check a point using one consistent parameter

Determine whether (−1,3,−3)(-1,3,-3) lies on the line in Example 21: r=(5,1,−2)+λ′(6,−2,1)\mathbf r=(5,1,-2)+\lambda'(6,-2,1), λ′∈R\lambda'\in\mathbb R, equivalently (x−5)/3=1−y=2z+4(x-5)/3=1-y=2z+4.

CJC · Lecture · Example 22

Choose a point on the line and a nonzero direction; keep one parameter consistent across all components.

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