Find the following for the vectors v = - 9 i + j and u = - 5 i + Squareroot11 j.

Question

Find the following for the vectors v = - 9 i + j and u = - 5 i + Squareroot11 j. vu, |v|, and |u| the cosine of the angle between v and u the scalar component of u in the direction of v the vector proj_vu v middot u = 45 + (Type an exact answer, using radicals as needed.) |v| = Squareroot82 (Type an exact answer, using radicals as needed.) |u| = 6 (Type an exact answer, using radicals as needed.) The cosine of the angle between v and u is (Type an exact answer, using radicals as needed.) The scalar component of u in the direction of v is [(Type an exact answer, using radicals as needed.)

Explanation / Answer

given v =-9i +j , u =-5i +11 j

v.u =(-9*-5)+(1*11) =45+11

|v|=[(-9)2+12]=(81+1)=82

|u|=[(-5)2+(11)2]=[25+11]=36=6

cos(v,u)=v.u/(|v||u|)

cos(v,u)=(45+11)/(682)

scalar component of u in direction of v =v.u/|v|

scalar component of u in direction of v =(45+11)/82

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