Require Help.

AraProdieur

1. The problem statement, all variables and given/known data
Vector A has a magnitude of 11 and points in the positive x-direction. Vector B has a magnitude of 22 and makes an angle of 32 degrees with the positive x-axis.
What is the magnitude of Vector A minus Vector B?


2. Relevant equations



3. The attempt at a solution

learningphysics

Can you describe where you're getting stuck and what you tried?

AraProdieur

I also have another question whereas it states: Use the method of components to find the magnitude and direction of the vector sum R1 where R1= A + B. The Vector A= 15.2 m at an angle alpha= 180 degrees from the positive horizontal axis, and Vector B = 17.2 m at an angle Beta= 41.3 degrees from the positive horizontal axis. Answer in meters. Answer in units of m.

What is the angle, theta 1, from the positive horizontal axis of the vector sum, R 1?

What is the magnitude of the vector difference R 2 where R 2= Vector A - Vector B?

What is the angle, theta 2, of the resulting vector?

What is the magnitude of the vector difference R 3 where R 3= B - A?

What is the angle, theta 3, of the resulting vector?

AraProdieur

I've only sketched it to get a graphical representation of the vectors, but other than that I have only gotten the resultant magnitude of A + B, but don't know how to get the resultant magnitude for A - B.

rootX

draw a llgm with two vectors A and B,
you have found one diagonal, just find other one, and it would be A - B

or,
reverse the direction of vector B

learningphysics

A - B is the resultant of A and (-B). Use the same approach as before except use -B instead of B...

another idea... draw both vectors originating from the same point... what is the vector joining the arrow ends of B and A?

AraProdieur

Yes, I know what you are referring to about the -B pertaining to its opposite direction, but the problem is I only know how to find the resultant magnitude for A + B and don't know how to find it for A - B because it's different since it's only two vectors and not more.

AraProdieur

Ok, so but isn't finding the magnitude of the resultant vector using basically the pythagorean theorem? If I use -B it will come out to the same answer. The thing that I'm confused about is that when I draw it graphically the A + B resultant vector looks shorter than the A - B resultant vector. So the problem is that I don't know how to find that A - B resultant vector, I only know the A + B resultant vector.

learningphysics

So you have drawn A - B, but are just having trouble calculating the magnitude?

learningphysics

No, the pythagorean theorem is only for right triangles... this isn't a right triangle... pythagorean theorem won't work for A-B or A + B.

AraProdieur

Yes, the way I depicted it was with Vector A going towards the right with a magnitude of 11 along the x-axis, while the -B is at 212 degrees going in the southwest direction with a magnitude of 22.

AraProdieur

? But I've used it before to determine the magnitude value of three vectors with their x and y coordinates provided.

learningphysics

Yes... from the x and y components, you can calculate the magnitude using the pythagorean theorem... That is because the x component is a vector in the x direction... the y component is a vector in the y direction... they are perpendicular and represent a right triangle...

if you calculate the x component (call it x) and y component (call it y) of A+B... then you can use the pythagorean theorem to calculate the magnitude... so maginitude = [tex]\sqrt{x^2 + y^2}[/tex] but this is not equal to [tex]\sqrt{A^2 + B^2}[/tex]

ie: A and B are not the x and y components of A+B...

AraProdieur

Oh, I see, so then how do I find the resultant magnitude of A - B?

learningphysics

Have you studied the law of cosines and the law of sines for triangles (non-right triangles)?

EDIT: You can also calculate the x-component of A-B, and the y-component of A-B... then use pythogrean theorem.

Both approaches are good... it's up to you...

AraProdieur

Yes, but I'm not very familiar with using it with the vectors.

AraProdieur

So the x/y component of Vector A would be <11,0>? and the vector component to find -B would be cos(212)= x/22? By which I would then use tan to find the y-component value?