Physics

Problem

Point

A

has coordinates

(1,2,0)\,\text{m}

and serves as a pivot for a uniform rigid bar. A force

\mathbf F = 4\mathbf i + 3\mathbf j - 6\mathbf k\,\text{N}

is applied at point

B

whose coordinates are

(5,-1,4)\,\text{m}

. An axis passes through

A

and is directed along the unit vector

\hat{\mathbf n} = \dfrac{2\mathbf i - \mathbf j + 2\mathbf k}{3}

. a. (i) Determine the torque vector about point

A

due to the applied force. b. (ii) Find the component (magnitude and sense) of this torque along the specified axis

\hat{\mathbf n}

. c. (iii) State, with reasons, whether the force tends to rotate the bar in the positive or negative sense about this axis.