A force $\vec F = 3\hat i + c\hat j + 2\hat k$ acting on a particle causes a displacement $\vec S = - 4\hat i + 2\hat j - 3\hat k$ in its own direction. If the work done is $6J$, then the value of $c$ will be
A force $\vec F = 3\hat i + c\hat j + 2\hat k$ acting on a particle causes a displacement $\vec S = - 4\hat i + 2\hat j - 3\hat k$ in its own direction. If the work done is $6J$, then the value of $c$ will be
$12$
$6$
$1$
$0$
A force $\vec F = 3\hat i + c\hat j + 2\hat k$ acting on a particle causes a displacement $\vec S = - 4\hat i + 2\hat j - 3\hat k$ in its own direction. If the work done is $6J$, then the value of $c$ will be
$W = \overrightarrow F .\overrightarrow s = (3\hat i + c\hat j + 2\hat k).( - 4\hat i + 2\hat j - 3\hat k)$$ = - 12 + 2c - 6$
Work done $ = 6J$ (given)
$\therefore $ $ - 12 + 2c - 6 = 6$$ \Rightarrow $ $c = 12$