Two co-terminus vectors $\vec a$ and $\vec b$ include at an angle of 60°. If $|\vec a|=|\vec b|=c$, then the length of the diagonal of the parallelogram formed by $\vec a$ and $\vec b$ that does not include the co-terminus point is
Answer & explanation
Correct answer: option 1
The length of the required diagonals is $|\vec a -\vec b|$.
Now,
$|\vec a -\vec b|^2=|\vec a|^2+|\vec b|^2-2(\vec a.\vec b)$
$⇒|\vec a -\vec b|^2=|\vec a|^2+|\vec b|^2-2|\vec a||\vec b|\cos 60°$
$⇒|\vec a -\vec b|^2=c^2 + c^2 - c^2 = c^2⇒|\vec a -\vec b|=c$