Understanding Vectors: Magnitude and Angle Calculation

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In summary, the conversation discusses a mathematical problem involving vectors and the calculation of their magnitude and angle in degrees. The problem is solved by using the equation tan-1(2/2) and the answer is 3 with an angle of 0 degrees. There is also a discussion about the use of j or i for imaginary numbers and the use of a calculator to solve the problem.
  • #1
Dx
[SOLVED] Vectors help?

The vector 2 + j2 is the same as what?

I know that j2 is -1 so the answer would be -2 for the magnitude but what about the angle in degrees? I don't comprehend the problem can anyone help make sense outta this for me, please!
Dx :wink:
 
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  • #2
A negative magnitude?

I'm sorry but I didnt understand your question very well.
 
  • #3
DX,
I don’t follow what you’re doing at all. That problem represents a point in a two-dimensional plane, and it is found in reference to both a horizontal and vertical axis. The first number is how far you move along the horizontal axis and the second is how far you move along the vertical. Because both numbers are positive, not negative, you will be going to the right 2 units and upward 2 units, placing the point in quadrant number one. Because the real part (2) and the imaginary part (j2) are of equal magnitude this is going to form a square, and the angle you will always get with a square is 45 degrees. But, the math goes like this;

C = 2 + j2
C = [squ][(2)2 + (2)2] = the magnitude you need to find.

And;

[the] = tan-1(2/2) = the angle you need to find.

In the equation to find the angle, where the 2/2 is located, the number that goes in the numerator will be the imaginary j value and the denominator will be the real value. This would have been easier to see if the values hadn’t been the same.

Hope that helps,
Good luck.

[edit]
I should expand a little about the square always having 45 degrees; If the point resides in quadrant one it is 45, in quad-2 it is 90 + 45, and so on.
 
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  • #4
Sorry to have confused everybody. I was trying to make sense outa this problem but didn't realize I confused you guys along with myslef. :wink:
I got it Boulderhead, THANKS!
Dx :wink:
 
  • #5
You're welcome!
Do you have a good calculator?
 
  • #6
Originally posted by BoulderHead
You're welcome!
Do you have a good calculator?

Its not the latest and greatest but me and my TI-83 have been though good times n bad. :wink:
Dx
 
  • #7
One thing that is confusing to me is your statement "I know that j2 is -1". This is a mathematics forum and mathematicians use i for the imaginary unit. Only electricians use "jmaginary" numbers!

Assuming that that is what you mean (and that you mean "^2" or squared rather than "j2") then 2- i^2= 2-(-1)= 3.

The "degrees" would be 0 since this is a real number.
 

1. What is a vector?

A vector is a mathematical quantity that has both magnitude (size) and direction. It can be represented graphically as an arrow pointing in a specific direction, with the length of the arrow indicating the magnitude of the vector.

2. How is the magnitude of a vector calculated?

The magnitude of a vector can be calculated using the Pythagorean theorem. Essentially, you square the x-component of the vector, square the y-component, add them together, and then take the square root of the sum. This will give you the length or magnitude of the vector.

3. What is the angle of a vector?

The angle of a vector is the direction in which it is pointing. It is typically measured in degrees or radians, with 0 degrees being the positive x-axis and 90 degrees being the positive y-axis.

4. How is the angle of a vector calculated?

The angle of a vector can be calculated using trigonometric functions, specifically the tangent function. You can use the x and y components of the vector to determine the ratio of opposite over adjacent sides, and then use the inverse tangent function to find the angle.

5. How are vectors used in real life?

Vectors are used in many real-life applications, such as in physics, engineering, and navigation. They can be used to describe the motion of objects, the forces acting on them, and the direction and magnitude of various quantities. They are also used in computer graphics, where they are used to represent the position and movement of objects in a 3D space.

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