Answer:
a) True
Explanation:
To calculate the moment produced by the force about point A, we can use the formula for the moment of a force about a point:
[tex]\[ \text{Moment} = \text{Force} \times \text{Lever Arm} \][/tex]
Given that the force
[tex]\( \mathbf{F} = -5\mathbf{i} + 3\mathbf{j} \)[/tex]
N is applied at point P, and point P is located 2 cm to the right of point A and 4 cm down, we can find the position vector
[tex]\( \mathbf{r} \)[/tex]
from point A to point P as follows:
[tex]\[ \mathbf{r} = 2\mathbf{i} - 4\mathbf{j} \][/tex]
The moment of the force about point A is then:
[tex]\[ \text{Moment} = \mathbf{F} \times \mathbf{r} \][/tex]
Using the cross-product formula:
[tex]\[ \mathbf{F} \times \mathbf{r} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ -5 & 3 & 0 \\ 2 & -4 & 0 \end{vmatrix} \][/tex]
[tex]\[ = (-5 \cdot 0 - 0 \cdot (-4))\mathbf{i} - (-5 \cdot 0 - 2 \cdot 0)\mathbf{j} + (-5 \cdot (-4) - 3 \cdot 2)\mathbf{k} \][/tex]
[tex]\[ = 20\mathbf{i} - 0\mathbf{j} + (-20 - 6)\mathbf{k} \][/tex]
[tex]\[ = 20\mathbf{i} - 26\mathbf{k} \][/tex]
The moment produced by the force about point A is
[tex]\( \mathbf{20i} - \mathbf{26k} \) N*cm.[/tex]
However, it's not clear from the question if the moment is clockwise or counterclockwise.
If we interpret "CW" as clockwise and "N*cm" as Newtons times centimeters, then the given moment of
[tex]\( \mathbf{2i} - \mathbf{26k} \) N*cm[/tex]
is indeed clockwise about point A. Therefore, the statement "The moment of the force about point A is
[tex]\( \mathbf{2i} - \mathbf{26k} \) N*cm CW" is:[/tex]
a) True
