Solving Vector Problems: Magnitude, Angle & Sum

[Moxin]

Two vectors are given by a = 7.4 x - 6.9 y and b = -18.8 x + 7.9 y.

1) What is the magnitude of a?

2) What is the angle between vector b and the positive x-axis?

3) What is the magnitude of the vector a + b?


I Have NO CLUE How to Even APPROACH this Problem. It's killin' me too because it looks SO EASY.. I was thinkin of trying to solve for a by the substitution method of solving a simultaneous equation..but then I'd be left with an answer with a variable in it..(?)..I'm really growing to hate physics with a passion!

 

[On Radioactive Waves]

1) What is the magnitude of a?


use the Pythagorean theorem. since you are given the vectors in component form, we have a right triangle and the magnitude is the hypotenuse

[squ](7.4²+6.9²)


2. given x and y, we know tangent. tan b = b_y /b_x

so arctan(y/x)=angle

and look to see which quadrent it lies into determine its respect to the x axis.



3. add the x compenents and add the y components to get the vector sum. this is a new vector, find the magnitude as shown in #1.

of course there are other ways of obtaing the same answers, these were the easiest ways to go about finding the answer with the given information, for me anyhow.

If you are still stuck or need to check the answers, post your work!

 

[HallsofIvy]

"I Have NO CLUE How to Even APPROACH this Problem."

At the risk of sounding harsh (a risk I regularly take),
did it occur to you to look up "magnitude" in the index of your textbook? I'll bet there is a formula for magnitude in the book.

Did you draw a picture (draw the vector on a coordinate system) and think about ways to calculate an angle. About the ONLY ways I know to calculate an angle from given lengths are to use inverse trig functions.

 

[Moxin]

Thanks RadioActive ! I didn't know magnitude was just the coefficient.


Halls, my textbook is a piece of crap and so is my professor's ability to communicate information (!) ..or maybe I'm jus stupid when it comes to physics/trig/math.. its prolly the latter :-\

 

[Sonty]

Originally posted by Moxin
Halls, my textbook is a piece of crap and so is my professor's ability to communicate information (!) ..or maybe I'm jus stupid when it comes to physics/trig/math.. its prolly the latter :-\

If you can't find that formula in your textbook then are you sure that it even is your physics/trig/math textbook?