Multivariable Calc: Vector equations, parametric equations, points of intersection

Only need detailed, step by step solutions for questions 1 and 11.

The rest just need final answers where indicated.

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  • Some of the answers showed up wrong, so I was wondering if you could double check questions 1 (the particles don't collide, but the paths DO intersect, as DNE was not correct for the points where the paths intersect), 11 (just the N(t) vector was incorrect), 10, and 14. Also, question 13 is missing if you could include the answer for it. Question 5 was written slightly wrong but that seemed like an unintentional writing mistake (it was t,3t^2, 5t^2+9t^4 instead of t,3t^2,3t^2+9t^4).

  • See my comments in the second file I just attached above and let me know if any of the solutions is not accepted by the website.

  • Thank you! The only error remained in 14. (3,12,-4) when t=-1, so the planes were parallel at the point (-1,-12,1). Thank you for your help.

  • You are absolutely right. I had r'(t) in front of my instead of r(t) to I had computed r'(1) instead of r(1). Sorry about that.

The answer is accepted.