Question

If you are given a line in vector form, and a plane in cartesian form, what is the best way to find a point of intersection?

Answer 1

I am kind of tired and not thinking clearly, but a plane would have two parameters in vector form and a line only has one. Would you solve for the single parameter in the line and then use that parameter in the equation of the plane?

Answer 2

I am honestly not sure where to start here

Answer 3

Find the perpendicular line vector between the planes if I recall. (may not be correct, calc iii was a long time ago)

Answer 4

This is actually form linear algebra, but I guess the concept is still the same

Answer 5

But I still don't know what to do here, our professor told us on this one...."hint you have not learned cross product in my class yet so it is not needed for this problem".

Answer 6

I think it had something to do with the gradient and unit vector. and linear algebra? Gosh, that was forever ago. I'm sorry I don't remember any more :( but @satellite73 could probably help

Answer 7

I feel like there is something with changing the parameter first, then setting them equal.

Answer 8

this may help http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-c-parametric-equations-for-curves/session-16-intersection-of-a-line-and-a-plane/MIT18_02SC_we_9_comb.pdf

Answer 9

That is exactly what I need, thank you

Answer 10

np, happy to help. I also found this and thought maybe it was the LA way, http://mathworld.wolfram.com/Line-PlaneIntersection.html