SOLUTION: Each of angles b/t the vectors u,v,& w is 60. ||u||= 4. . ||v||=2 & ||w||=6 Then find ||u+v+w||

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Question 1183181: Each of angles b/t the vectors u,v,& w is 60. ||u||= 4. . ||v||=2 & ||w||=6
Then find ||u+v+w||
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Use the fact that abs%28u%29%5E2+=+u%2Au+ and u%2Av+=+abs%28u%29abs%28v%29cos%28theta%29, where abs%28u%29 is the magnitude of the vector u, and u%2Av is the dot product of the vectors u and v.
Then , by direct application of the distributive, commutative, and associative properties.
Now


= since theta%5B1%5D+=+theta%5B2%5D+=+theta%5B3%5D+=+60%5E0

=, since cos60%5E0+=+1%2F2

= 16 + 4 + 36 + 8 + 12 + 24 = 100.

==> abs%28u%2Bv%2Bw%29%5E2+=+100 ===> highlight%28abs%28u%2Bv%2Bw%29+=+10%29