Let u and v be two voctors in R. (a) Prove that ||u+v|| + ||uv|| =...

 

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Let u and v be two voctors in R³. (a) Prove that ||u+v||² + ||uv||² = 2||u||² +2||v||². (b) Prove that u v = ||u+v||²||uv||² (c) If ||u|| = √2, |v|| = √3, and u v = 1, find ||u+v||. (d) Prove that there are no vectors u and v such that ||u|| = 2, |v|| = 3 and u-v=7. Let u and v be two voctors in R³. (a) Prove that ||u+v||² + ||uv||² = 2||u||² +2||v||². (b) Prove that u v = ||u+v||²||uv||² (c) If ||u|| = √2, |v|| = √3, and u v = 1, find ||u+v||. (d) Prove that there are no vectors u and v such that ||u|| = 2, |v|| = 3 and u-v=7.