Vectors question- quite confused?

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A point object is acted on by a force of 5.0 N acting due East and a force of 12.0N acting 60 degrees north of due West. Use the parallelogram method to calculate the magnitude and length of the resultant.

http://gyazo.com/660a89d21cc639d7299f20d…

In the parallelogram method isn't the resultant the diagonal? But in the book it isn't the case because the resultant is this...

http://gyazo.com/b344f2c788218c304b305c9…

Could somebody explain why please?

I don't know what exactly your question is, but basically you just have to break those vectors up into their i, j, and k components, and add those puppies up! If it wants direction in terms of angles instead of i/j/k, then you can just use sin/cos/tan to get whatever angle you want at the end. And since it wants magnitude, you have to do that at the end too by adding the squares of the components and taking the square root.

Edit: Actually I just googled parallelogram method and it's completely different (I'd still use my method, it's so much easier!). But basically you do the exact same thing but with pictures instead of algebra.

Those links don't work btw

I would also resolve the forces into the x, y and z parts, then add them up and then work out the overall force.

You could use the ideas in AC theroy to deal with it.

If everything is in a 2D universe then treat the north/south part as the resistive part and the east/west as the reactive part. Then use the classic equations for impedance calculations to deal with it. Treat the two forces as if they were electrical currents flowing in a AC circuit.

Man this is a blast from the past but I'll take a wild guess that it's:

Magnitude = (169-120(cos60))^(.5) = 10.44 length. The method ur gonna use is called the "law of cosines" actually for both of them... Btw magnitude means length so like i think u mean
direction = 144 = 109+25 - 10.44 (cos(x)); cos(x) = -.1(sqrt109); x - 96 degrees = 84 deg north of due west

so its gonna be 10.44 N, 84 deg N of due west

What really trips a lot of people up, and what tripped me up when I encountered these kinds of problems before is the whole degrees of west thing because I have a hard time visualizing word problems.

The parallelogram method is a step more advanced than the other method I'm not sure what it's called, but putting them together and taking the diagonal thing.

Remember the take home here is that variant on the Pythagorean formula, the "Law of Cosines" A^2 = B^2 + C^2 - 2BC Cos (A). Angle A is of course the one opposite of the side A.

Hey guys, she doesn't want the vectors to broken up into x an y components or to use trigonometry. His question was to use the parallelogram method, which means drawing an accurate diagram to scale and measuring the resultant vector with a ruler. Personally, I think that breaking the vectors up into components is a lot easier but the parallelogram method was the one that I was first taught to use when I was still in high school.

Last edited by Jono on 20 Jul 2013, 3:12 pm, edited 1 time in total.

Ok, so what you have to do in the parallelogram method is to first choose scale, take 1 N = 1 cm. Now, draw a line 5 cm in length, with an arrow pointing right. That represents your 5.0 N vector due east. Now, place the centre of your protractor on the right edge of the arrow you've just drawn and mark off a 60 degree angle as measured from the line (remember that the direction of east wast from left to right and so west is the opposite direction, so you want to measure a 60 degree angle upward from the west direction). Now, hold your ruler starting from the right edge of the arrow you've just drawn and draw another line 12 cm long through your marking where you marked off your 60 degree angle. The direction of the vector in this case, will be pointing along that line away the first one you drew, so make the arrow point in that direction. Parallel dotted lines drawn at the opposite ends make up the 2 other sides of your parallelogram. The diagonal of the parallelogram drawn from left edge of 5 cm line to the top edge of the 12 cm line represents your resultant vector. The direction of the vector, I think, will point upward along that diagonal from the left edge of the 5 cm line to the top edge of 12 cm, measure it with the protractor to get it in degree. Also, the length of the line in cm, as measured with your ruler, will give you the magnitude of your resultant force in newtons.

Your links won't work for me but I can guess that in your textbook probably shows the resultant vector as a side of a triangle. The answer is that you can always make a parallelogram from your first 2 vectors by drawing dotted lines on opposite sides parallel to them and of the same length. In that case, the resultant force is always represented by a diagonal of the parallelogram.