Final answer:
The moment about the origin can be determined using the formula M = r x F, where r is the position vector and F is the force vector. Substituting the given values and expanding the cross product, the moment is -12i + 7j - 1k.
Step-by-step explanation:
To determine the moment about the origin, we can use the formula:
M = r x F
Where r is the position vector and F is the force vector.
In this case, the position vector r = i + j + k and the force vector F = -i -2j + 5k.
Substituting these values into the formula, we have:
M = (i + j + k) x (-i -2j + 5k)
Expanding the cross product, we get:
M = (1 * (-2) - 2 * 5)i + (1 * 5 - (-2) * (-1))j + (1 * (-1) - (-2) * (-1))k
M = -12i + 7j - 1k
Therefore, the moment about the origin is -12i + 7j - 1k.