Unit vectors

[macostar]

Hi, I'm stuck with question two. If anyone could help me would be greatly appreciated.
Thanks.

[kinslayer]

Hi,

For i), use the unit circle and basic trigonometry. u = cos ai + sin aj, etc.

ii) is just straightforward dot products: u.v = cos a * cos b + sin a * sin b etc.

For iii), use the alternate definition of cross products, u.v = ||u|| * ||v|| * cos t, where t is the angle between u and v. Calculate u.v and u.w in this way and set them equal to the results from ii).

hints: cos(-t) = cos t, sin(-t) = -sin(t), and if two vectors make angles of a and b with the i-axis, respectively, then the angle between them is a - b.