Question

Determine the moment of the force F about point P. Express the result as a Cartesian vector. Express your answer in terms of the unit vectors i, j, and k. Use the 'vec' button to denote vectors in your answers. Express your answer using three significant figures.

Answer 1

(M_f)p = -24 i + 24 j + 8 k

Step-by-step explanation:

Given:

F = 2 i + 4 j - 6 k

Find:

- Moment of the force F about point P. (M_f)p

Solution:

Step 1: Compute vec(PA)

vec (P) = -2 i - 3 j + 2 k

vec (A) = 3 i + 3 j - 1 k

Hence, vec (PA) = vec(A) - vec(P)

vec (PA) = (3 i + 3 j - 1 k) - (-2 i - 3 j + 2 k)

vec (PA) = 5 i + 6 j - 3 k

Step 2: Compute (M_f)p

(M_f)p = vec (PA) x F

`(M_f)_p = \left[\begin{array}{ccc}i&j&k\\5&6&-3\\2&4&-6\end{array}\right] = \left[\begin{array}{c}-24\\24\\8\end{array}\right]`

Hence,

(M_f)p = -24 i + 24 j + 8 k