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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: macostar on February 28, 2014, 08:25:10 pm

Title: Unit vectors
Post by: macostar on February 28, 2014, 08:25:10 pm

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

Title: Re: Unit vectors
Post by: kinslayer on March 03, 2014, 05:54:28 pm

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.