Problems from Sum and subtract of vectors

Given the vectors u=(3,2) and v=(1,5), determine:

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Development:

  • 3u2v=3(3,2)2(1,5)=(9,6)+(2,10)=(11,16)
  • uv=(3,2)(1,5)=(2,3)
  • 5u+2v=5(3,2)+2(1,5)=(15,10)+(2,10)=(13,0)
  • u+3v=(3,2)+3(1,5)=(0,13)

    |(11,16)|=112+(16)2=121+256=377|(2,3)|=(2)2+(3)2=4+9=13|(13,0)|=132+02=169=13|(0,13)|=02+132=169=13

    We can see, then, that none of these norms is one. Therefore, none of these vectors are unit vectors.

Solution:

  • (11,16)
  • (2,3)
  • (13,0)
  • (0,13)

    None of these vectors is a unit vector.

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