Three forces act on an object. two of the forces are at an angle of 95◦ to each other and have magnitudes 35 n and 7 n. the third force is perpendicular to the plane of these two forces and has magnitude 9 n. calculate the magnitude of the force that would exactly counterbalance these three forces. round your answer to one decimal place.

We want to find such that the object needs is in equilibrium:

We're told that , , and . We also know the angle between and is 95º, which means

is perpendicular to both and , so .

If we take the dot product of with the sum of all four vectors, we get

We can do the same thing with and :

Finally, if we do this with , we get

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: