a calculus 3 homework problem

🌟Support the channel🌟

🌟my other channels🌟

🌟My Links🌟

🌟How I make Thumbnails🌟

🌟Suggest a problem🌟

[hallfiry]

Here's how it's taught in Bavarian high schools:
1) Set x=t
2) Solve for y and z:
y=1.5t-2
z=3.5t-5
3) r(t) = <t, 1.5t-2, 3.5t-5>
4) Optional: separate into a constant vector and multiple of t:
r(t)=<0, -1, -5> + t<1, 1.5, 3.5>

[martinb]

Should be "perpendicular to each of the normal vectors", not "each of the planes", right?

[gragasapmidlane]

Cover : *calc 3*

Looks inside : A levels maths

[HenkVanLeeuwen-io]

There is a typo in the email above.
It should be y-z=3-2x, 3y+z=1-x.
So 4y=4-3x.
So y=1-0.75x, z=1-x-3+2.25x=3.25x-2.

[cowgomoo]

so if im understanding properly: you just set x=0 because it's likely that the line of intersection will cross the x=0 plane at some point. However aren't there cases where the line of intersection is parallel to the x=0 plane? is there anything we can do to see if this is the case? is there anything about this problem specifically that makes it clear that we can just set x=0? if so, what?

it's clear geometrically that the line of intersection MUST cross either the x=0 plane, the y=0 plane, or the z=0 plane. Should we just guess these one by one until we get a system of equations that works?