1-The projection of u = ? ?5,?4,?5 ? along v = ? ?2,4,?5 ? is 2- Angle theat bet

Question

1-The projection of u=??5,?4,?5? along v=??2,4,?5? is

2-Angle theat between two planes is defined to be the angle between their normals which satisfies 0?theat<? (see the figure).

http://webworks2.csuohio.edu/webwork2_files/tmp/CSU_MTH283spr14/img/dbcf3d51-9b17-3596-9e2b-69458cab63b9___340d304c-d122-3d74-9539-5714f46be012.png

Consider two planes with normal vectors n1=??3,3,1? and n2=?3,?2,?3?. For these planes and angle theat between them, we

Cos(theat)=

3) If point P has rectangular coordinates (5,5,?9), then its cylindrical coordinates are

(r,theat,z)=

The projection of u=??5,?4,?5? along v=??2,4,?5? is Angle theat between two planes is defined to be the angle between their normals which satisfies 0?theat

Explanation / Answer

u.v=10-16+25=19

u.v/|v|*|u|=.3486

scalar projection of u along v is |u|*.3486=2.832

vector projection is 2.832*v/|v|=.422*v

2)n1.n2=-18

cos()=n1.n2/|n1||n2|=-.88

3)cylindrical coordinates are(7.07,pi/4,-9)

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