Question

sketch the curve with the given vector equation. Indicate with arrows the direction in which t increases:
r(t)=costi - costj + sintk

Answer 1

@harkan is it is a spehere of unit radius with centre at (1,-1,1)

Answer 2

I'm not sure, according to http://openstudy.com/study#/updates/4e28c1270b8b3d38d3b92609 it's an ellipse with center (0,0,0). I don't understand how he got to that answer though.

Answer 3

ultimately, you make a table with t values in one column and r(t) vectors in the other column and then plot, point for point.
I was seeing a wobbly circle... but with more points, I wouldn't be surprised if it is an ellipse.

Answer 4

I guess the sin and cos give a circle in the usual way (in x and z) so then what does the additional cos in y do?

If it was just t instead of cos t then that would produce a helix as t varied, whereas cos t is going to oscillate...