The vertices of a quadrilateral are `A(1,2,-1), B(-4, 2,-2), C(4,1,-5)` and `D(2,-1, 3)`. Forces of magnitude `2,3,2N` are acting at point `A` along the lines `AB, AC, AD` respectively.Find their resultant.

Options

A. `(10hati-9hatj+6hatk)/(sqrt(26))`
B. `((hati-9hatj-6hatk)/(sqrt(26)))`
C. `(hati-9hatj+16hatk)/(sqrt(26))`
D. `(hati-19hatj+6hatK)/(sqrt(26))`

Explanation

To solve the problem of finding the resultant force acting at point A due to the forces along lines AB, AC, and AD, we will follow these steps:

### Step 1: Determine the position vectors
The position vectors of points A, B, C, and D are given as:
- \( \vec{A} = (1, 2, -1) \)
- \( \vec{B} = (-4, 2, -2) \)
- \( \vec{C} = (4, 1, -5) \)
- \( \vec{D} = (2, -1, 3) \)
...