Answer:
For the system of forces to be in equilibrium, the vector sum of the forces must be equal to zero. Therefore, we can set up the following equation:
(2i-j+k) + (3i+4j+4k) + (5i+3j+3k) = 0
We can also express the force vectors in terms of the position vectors of the points at which they act as follows
F = (3i+2k)×(2i-j+k) + (4i-5j+ak)×(3i+4j+4k) + (-4i-2j+4k)×(5i+3j+3k) = 0
Expanding and simplifying the equation we get
3i+2k - 2j + k - 4i +5aj +4k -5j +4k +5i +3j -3k = 0
-i +3j +3k +5aj = 0
Therefore, a = -1/5
The value of a is -1/5.