http://imgur.com/pGQj9z5Please give in detail how you found your answer. I appre

Question

http://imgur.com/pGQj9z5Please give in detail how you found your answer. I appreciate it!

The angle between u rightarrow and w rightarrow is pi/3, and assume that |u rightarrow| = 2, and |w rightarrow| = 3. The goal of this exercise is to find the angle between u rightarrow and u rightarrow - 2 w rightarrow. Calculate (u rightarrow - 2w rightarrow) middot (u rightarrow - 2w rightarrow). Calculate |u rightarrow - 2 w rightarrow|. Calculate u rightarrow middot (u rightarrow - 2w rightarrow). Find the angle between u rightarrow and u rightarrow - 2w rightarrow.

Explanation / Answer

u.w = |u||w|cos(pi/3) = 2*3*0.5 = 3 a) (u-2w).(u-2w) = u.u - 4u.w + 4w.w = 4 - 12 + 36 = 28 b) |u-2w| = sqrt(28) = 5.29 c) u.(u-2w) = u.u - 2u.w = 4 -6 = -2 d) Angle = cos^-1( -2/(2*5.29)) = cos^-1(-0.189) = 79.1 degrees

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