Finding Orthogonal Projection of a Curve in the yz-Plane

[hungryhippo]

How would you approach a question where you're given a curve in terms of a scalar equation, and asked to find the orthogonal projection of this curve in the yz-plane

You know that the curve is the intersection of the surfaces of:

x=y^2+z^2 --1
x-2y+4z=0 --2

From here, I would just substitute equation 1 into 2 for x, to find the resulting curve

I know that a yz-plane indicates that the x-coordinate will always be 0 , so (0,y,z)
For scalar projections, you can find it as just

(a) dot (b) / (length of a)

I'm not sure if what I'm thinking so far is correct, and extremely unsure on the projection part.

I really need help on this

Thanks in advance for any advice

 

[Dick]

You are probably just over thinking this whole thing. Once you've found a yz curve by eliminating x, you are done, right? Projection into the yz plane just means ignore the x value. You don't need a projection formula for this case.