express a in terms of its components?

Question

suppose a is a three dimensional unit vectorin the first octant that starts at the origin and makes angles of 55 degrees and 80degrees with the positive x and y axes respectively. express a in terms of its components.

ok we did a similar example in class and i followed it and used

a=cos55i+cos88j+____k

i got the answer to be <.57, .17, .75> but that is wrong. If you could maybe point out where i went wrong. THanks

Answer 1

It looks like your theory is correct, you just made a computational error somewhere. You haven't posted your intermediate steps, so I can't tell you exactly where, but here is the correct computation:

cos 55° ≈ 0.57358
cos² 55° ≈ 0.32899
cos 80° ≈ 0.17365
cos² 80° ≈ 0.03015

1-cos² 80°-cos² 55° = 0.64086
a_z = √(1-cos² 80°-cos² 55°) ≈ 0.80053

So the answer would be approx. <.57358, .17365, .80053> -- the last entry being closer to .8 than .75.