Two forces $P + Q$ and $P -Q$ make angle $2 \alpha$ with each other and their resultant make $\theta$ angle with bisector of angle between them. Then :
$P\, tan\, \theta = Q\, tan \, \alpha$
$P\, sin\, \theta = Q\, sin\, \alpha$
$P\, cos\, \alpha = Q\, sin\, \theta$
$P\, sin\, \alpha = Q\, sin\, \theta$
A displacement vector of magnitude $4$ makes an angle $30^{\circ}$ with the $x$-axis. Its rectangular components in $x-y$ plane are .........
There are four forces acting at a point $P$ produced by strings as shown in figure, point $P$ is at rest. The forces $F_1$ and $F_2$ are respectively:-
A vector $\vec Q$ which has a magnitude of $8$ is added to the vector $\vec P$ which lies along $x-$ axis. The resultant of two vectors lies along $y-$ axis and has magnitude twice that of $\vec P$. The magnitude of is $\vec P$
The magnitude of pairs of displacement vectors are given. Which pair of displacement vectors cannot be added to give a resultant vector of magnitude $13\, cm$?
Explain the resolution of vector in three dimension.