Solving Vector Problems: Magnitude, Angle & Sum

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In summary, two vectors are given by a = 7.4 x - 6.9 y and b = -18.8 x + 7.9 y. The magnitude of vector a can be found using the Pythagorean theorem, since it is given in component form. The angle between vector b and the positive x-axis can be found using inverse trig functions. The magnitude of the vector a + b can also be found using the Pythagorean theorem, by adding the x and y components of the two vectors. It is important to refer to a good textbook and to draw a picture to approach these types of problems.
  • #1
Moxin
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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!
 
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  • #2
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 = by /bx

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!
 
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  • #3
"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.
 
  • #4
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 :-\
 
  • #5
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?
 

1. What is a vector?

A vector is a mathematical quantity that has both magnitude (size or length) and direction. It is represented by an arrow, where the length of the arrow represents the magnitude and the direction of the arrow represents the direction of the vector.

2. How do you calculate the magnitude of a vector?

The magnitude of a vector can be calculated using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squared components of the vector. For example, if a vector has a horizontal component of 3 and a vertical component of 4, the magnitude would be calculated as √(3² + 4²) = √(9 + 16) = √25 = 5.

3. How do you calculate the angle of a vector?

The angle of a vector can be calculated using trigonometric functions such as sine, cosine, and tangent. To find the angle, you can use the inverse tangent function (arctan) to find the ratio of the vertical component to the horizontal component of the vector. The resulting angle will be in radians, so you may need to convert it to degrees if necessary.

4. Can you add or subtract vectors?

Yes, you can add or subtract vectors by combining their respective components. To add two vectors, you simply add their horizontal and vertical components separately. Similarly, to subtract two vectors, you subtract their horizontal and vertical components separately.

5. What is the difference between vector addition and scalar multiplication?

Vector addition involves adding two or more vectors to create a new vector, while scalar multiplication involves multiplying a vector by a scalar (a real number). In vector addition, the resulting vector will have both a magnitude and direction, while in scalar multiplication, the resulting vector will have the same direction as the original vector but its magnitude will be multiplied by the scalar.

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