Two forces represented by the vectors F1 1 53 and F2 40 1

Two forces, represented by the vectors F_1 = (1, -5,3} and F_2 = (4,0, - 1), are acting on an object. Give a vector F representing the force that must be applied to the object if it is to remain stationary.

Solution

Given that two forces F₁ and F₂ where F₁=i-5j+3k and F₂=4i-k.

Then the net forces is given by the sum of the two vectors. i.e. F₃=F₁+F₂=(i-5j+3k)+(4i-k)=5i-5j+2k

To object remain stationary, we find F such that F+F₃=0.

So F=-5i+5j-2k