Let \(\left| {\vec a} \right| \ne 0,\left| {\vec b} \right| \ne 0.\)
\(\left( {\vec a + \vec b} \right).\left( {\vec a + \vec b} \right) = {\left| {\vec a} \right|^2} + {\left| {\vec b} \right|^2}\)
Holds if and only if
1
\(\vec a\) and \(\vec b\) are perpendicular
2
\(\vec a\) and \(\vec b\) are parallel
3
\(\vec a\) and \(\vec b\) are inclined at an angle of 45°
4
\(\vec a\) and \(\vec b\) are anti-parallel