Doing MIT OCW 18.06 using Gilbert Strang Intro to Linear Algebra.(adsbygoogle = window.adsbygoogle || []).push({});

Ch 1.2

The vectors that are perpendicular to <1,1,1> and <1,2,3> lie on a ___________.

I would have said "plane".

I've worked with vectors in calculus, and if you take the cross product of those two vectors you get a vector perpendicular to both, and you could, visualizing it, move that vector around on the surface of the plane defined by <1,1,1> and <1,2,3>...

But the answer given in the solution manual is "line"...

How are all the vectors perpendicular to <1,1,1> and <1,2,3> lying on a line?

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