Math Is Fun Forum

sk

Member

Registered: 2006-08-04

Posts: 19

Vectors!!!!!!!!!!!!!!!! Need Help

Help me in solving this problem using the graphical and the analytical method: Vector A is 60 Newton 20 degrees south of west, Vector B is 80 Newton North, and Vector C 70 Newtons 80 degrees North of east. Find the the direction and the magnitude of the resultant vector 

Last edited by sk (2008-07-01 22:44:05)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Vectors!!!!!!!!!!!!!!!! Need Help

To answer the question graphically, draw the vectors joined together.
So, draw a line of length 60 that is 20 degrees south of west. Then starting at the end of that line, draw a northward line of length 80, and similarly draw vector C starting at the end of vector B.

Now draw a line from the start of vector A to the end of vector C that you've just drawn, and the length and angle of this line will be the combined length and angle of the other three vectors.

To answer it analytically, think of each vector as having vertical and horizontal components, rather than length and angle. This way, they're much easier to add up.

Vector A is 60N and points 20 degrees south of west.
This means that (taking north and east as positives) the horizontal component is -60cos(20), and the vertical component is -60sin(20).

Vector B is easier - its horizontal component is 0 and its vertical one is 80.
You can work out the components for Vector C similarly to how Vector A was worked out.

After you have the vertical and horizontal components for each vector, simply add them all up to get the components of the final vector. You can convert back to length and angle from here by using Pythagoras and inverse tan respectively.

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Why did the vector cross the road?
It wanted to be normal.