When the resolution of vector is required ?

 

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Explain resolution of vector in two dimension. Explain resolution of vector in its perpendicular components.

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 :

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 $\vec P$

Following forces start acting on a particle at rest at the origin of the co-ordinate system simultaneously${\overrightarrow F _1} = - 4\hat i - 5\hat j + 5\hat k$, ${\overrightarrow F _2} = 5\hat i + 8\hat j + 6\hat k$, ${\overrightarrow F _3} = - 3\hat i + 4\hat j - 7\hat k$ and ${\overrightarrow F _4} = 2\hat i - 3\hat j - 2\hat k$ then the particle will move

The direction cosines of vector $( A - B )$, if $A =2 \hat{ i }+3 \hat{ j }+\hat{ k }, B =2 \hat{ i }+2 \hat{ j }+3 \hat{ k }$ are