Vectors

Question 1

How to say why for sure the planes meet at a pint

Answer 1

Det is not 0 so matrix has an inverse so the equations have a unique soltuon, meaning planed meet at one point

Question 2

If all your points take on the form of a parameter , how can you show this is a LINE

Answer 2

split it up into normal number + lambda (Coe friends of lambda)

This is lit a line DONT LACK

Question 3

When two planes intersect at a line, what kind of line is it (3d)

Answer 3

IT IS 3D LINE, don’t lack and think it’s 2D!

Question 4

What’s the DIRECTION VECTOR of the line of intersection of 2 planes and why?

Answer 4

It is the CROSS PRODUCT of their NORMALS!!, because think about IT THE line is perpendicular to both normals! So it works

So use this, as well as a point of intersection of the planes to make the line!