SOLUTION: Show that 4u · v = ||u + v||^2 − ||u − v||^2. Show that u and v is orthogonal if and
only if ||u + v|| = ||u − v||.
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Question 1203665: Show that 4u · v = ||u + v||^2 − ||u − v||^2. Show that u and v is orthogonal if and
only if ||u + v|| = ||u − v||.
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
Show that
Hint. , so
=
=
=
=
=
=
Show that u and v is orthogonal if and only if
If and are orthogonal vectors, then:
now , but the norm is ever positive therefore:
.
now, if we have:
By the equality
<=> <=>
this means and are
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