If ax + by + cz = 0 is plane through origin in R3, prove that two planes through the origin share infinite points in common.
I'm not sure how to get this one.
First Year Linear Algebra -Common points of planes through the origin
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linear-algebra
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2Hint: Two homogeneous equations in three variables always have a free variable and hence a nontrivial solution. – 2017-02-10
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0@MichaelBurr awesome, thanks. – 2017-02-10
1 Answers
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Your planes are $\underline{r}\cdot \underline{n}_1=0$ and $\underline{r}\cdot \underline{n}_2=0$
Then $\forall\lambda\in\mathbb{R}$, $\underline{r}=\lambda\underline{n}_1\times \underline{n}_2$ satisfy both equations.