Consider two nonzero vectors $a$ and $b$.
First, if $|a+b|=|a-b|$, how can I show that $a$ and $b$ are perpendicular?
And how can I show that $|a\times b|^2 = |a|^2 |b|^2 - (a\cdot b)^2$ ?
$a\cdot b$ is the dot product.
Consider two nonzero vectors $a$ and $b$.
First, if $|a+b|=|a-b|$, how can I show that $a$ and $b$ are perpendicular?
And how can I show that $|a\times b|^2 = |a|^2 |b|^2 - (a\cdot b)^2$ ?
$a\cdot b$ is the dot product.
For the first, square both sides and see what cancels out. If two vectors are perpendicular, what is their dot product?
For the second, remember that $a \cdot b = \|a\|\|b\|\cos{\theta}$. Plug in and use a trigonometric identity to change $\cos$ to $\sin$.