At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
The initial instinct is to just add the two vectors together to get R. And here's why I think it's not going to work out: |dw:1446875853534:dw| Intuitively, adding V1 and V2 would obviously NOT give you the answer! If you add V1 and V2 together, the resultant you get from the addition would be a greater than the resultant you're supposed to get!
Instead, notice how it's a triangle. Given the values of each "leg" of the triangle, you can easily find the value of V1 and V2. And now you might be asking: now what? Recall your cosine rule. You can use it when you're given a triangle that doesn't contain special properties (e.g. triangles with 90-degree angles, isosceles triangles). All you need is the value of two sides and the angle in between! (See the attachment.) You can then find the angle in between V1 and V2 by finding the angles like so: |dw:1446876573616:dw| And you know that a line is 180-degrees across! I hope this helps.
@mortonsalt, please clarify if I've misunderstood what you said above, bus far as I can tell, it's ok to add the two force vectors to find the a third vector that will produce equilibrium. This is ok as long as you realize that you need to reverse the DIRECTION of the resultant vector in order to produce the equilibrium vector you want. This isn't a big deal for this question because you're only asked to find magnitude. For instance, If you wanted to balance each force separately, you would just add an equal but opposite force. Add those two opposite forces together, and you get the equilibrium vector that is equal in magnitude but opposite in direction to the resultant vector of your original two forces. Also, since your starting forces have whole number magnitudes plotted on a convenient grid, you don't need to consider angles at all. If you add the two vectors in the diagram, the resultant can be deconstructed into a right triangle that has a (+2)+(+4)=+6N x-component and a (+3)+(-1)=+2N y-component. By the Pythagorean Theorem, the hypotenuse (i.e. the magnitude of the resultant) is about 6.3N (answer C). The equilibrium vector would also have this magnitude, but would have exactly the opposite direction (i.e. -6N x-component and -2N y-component).
@matt101 Hello, thank you for checking this out! I guess I wasn't exactly clear about that, which was my bad. But yes, that's what I was trying to say. I forgot that there was a grid to begin with! Hahaha, I was working on with a separate sheet of paper. I've attached a picture below that shows the vector diagram which, in turn, shows that the x-component is 6 and the y-component is 2.