I am attempting problem number 21 and have come across trouble on part C. To solve the problem, I combined the vectors from part A and B to get the vector for part C and I got the right answer for the second coordinate but not for the other two coordinates so I'm not sure what I'm doing wrong. Thank you in advance for your help!
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A)Well, P is on the y-axis so x=z=0, which means that P is in the second plane(why??), and in the first plane means that 5y=1 so y=1/5--it sounds like you figured this out.
B) A unit vector parallel to both planes will be perpendicular to both normals (what *are* the normal vectors to each plane, and how do you use them?), which turns out to be something parallel to
±(i+0j-k),
so a unit vector that's has positive first coordinate would be (i+0j-k)/√2.--it sounds like you got this part too.C) there are a lot of vector equations that will do the job for this part, but the simplest one for you to write would be r(t)=<0,1/5,0> + t<1/√2,0,-1/√2>=(t/√2i+1/5j-t/√2k).
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