Question

I'm misunderstanding some elementary concept. Question 2 - http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-c-parametric-equations-for-curves/session-15-equations-of-lines/MIT18_02SC_pb_17_comb.pdf

I'm failing to follow the reasoning where it says the line of intersection is perpendicular to both normals.

Now, this seems to assume the coefficients of (1,1,1) and (1,2,3) are both normals. However, I thought by the very definition of the dot product, two vectors are perpendicular (ie: one is normal) if and onl

Answer 1

if and only if their dot product is 0. Clearly in this question the two dot products are not equal to 0, they are equal to 1 and 2 respectively. How then can be treat these two coefficient vectors as being normals when their respective dot products with <x,y,z> does not equal 0?

Answer 2

I would like to both be shown where my reasoning is wrong and to also gain a full geometric visualization of what is happening here.

Answer 3

I would like to both be shown where my reasoning is wrong and to also gain a full geometric visualization of what is happening here.