Simple Vector Difference Question

In summary, the conversation discusses the vectors A = 2.00i + 600j and B = 3.00i - 200j, and the vector sum C = A + B and vector difference D = A - B. The values of C and D are calculated to be 5.00i + 4.00j and -1.00i + 8.00j, respectively. The conversation also mentions graphing the vectors by drawing arrow segments in the Cartesian plane to represent them and showing the geometric method of adding the vectors.
  • #1
CoolMan
1
0
Given the Vectors A = 2.00i +600j and B=3.00i -200j, (a) draw the vector sum C= A+B and the Vector difference D=A-B (b) calculate C and D, first in terms of unit vectors and then in terms of polar coordinates, with angles measured with respecy to + x axis.

This is wat I got so far
C = A+B
= 5.00i+4.00j

D= A-B
= -1.00i+8.00j

How do I graph it and etc..
 
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  • #2
I think when it says draw them, it wants you to draw arrow segments in the cartesian plane to represent the vectors, and show the geometric way of adding the two vectors.
 
  • #3


I would like to provide a more detailed response to the given content. Firstly, let's define what a vector is. A vector is a mathematical quantity that has both magnitude and direction. In this case, the vectors A and B have magnitudes of 2.00 and 3.00 respectively, and their directions are given by the unit vectors i and j. The unit vectors i and j represent the x and y directions respectively.

(a) To graph the vector sum C and the vector difference D, we can use a coordinate system with the x-axis and y-axis representing the i and j directions, respectively. The vector C can be drawn by starting at the origin (0,0) and moving 5 units in the i direction and 4 units in the j direction. This gives us a vector that starts at (0,0) and ends at (5,4). Similarly, the vector D can be drawn by starting at the origin and moving -1 unit in the i direction and 8 units in the j direction. This gives us a vector that starts at (0,0) and ends at (-1,8). The graph for C and D would look like this:

[INSERT IMAGE HERE]

(b) Now, let's calculate the vectors C and D in terms of unit vectors and polar coordinates. To do this, we can use the Pythagorean theorem and trigonometric functions.

For the vector C, we can use the formula C = A + B, which gives us:

C = (2.00i + 600j) + (3.00i - 200j)

= (2.00 + 3.00)i + (600 - 200)j

= 5.00i + 400j

Using the Pythagorean theorem, we can calculate the magnitude of vector C as:

|C| = √(5.00^2 + 4.00^2)

= √(25 + 16)

= √41

Therefore, the polar coordinates for vector C would be (|C|, θ) where θ is the angle formed by the vector with the positive x-axis. To calculate θ, we can use the inverse tangent function (tan^-1):

θ = tan^-1(4.00/5.00)

= 38.66°

Therefore, the polar coordinates for vector C would be (√
 

1. What is a simple vector difference?

A simple vector difference is the calculation of the difference between two vectors using basic vector subtraction. It involves subtracting the corresponding components of the two vectors to find the resulting vector.

2. How is a simple vector difference calculated?

To calculate a simple vector difference, you simply subtract the components of the second vector from the components of the first vector in the same order. For example, if vector A = (2, 4) and vector B = (1, 2), the simple vector difference would be A - B = (2-1, 4-2) = (1, 2).

3. What is the difference between a simple vector difference and a complex vector difference?

A simple vector difference only involves two vectors with the same number of components, while a complex vector difference involves multiple vectors with varying numbers of components. The process of calculating a complex vector difference is more involved and may require additional mathematical operations.

4. What are some real-world applications of simple vector difference?

Simple vector difference can be used in a variety of fields, such as physics, engineering, and computer graphics. It can be used to calculate displacement, velocity, and acceleration in physics problems, to determine the forces acting on an object in engineering problems, and to create graphics in video games and animations.

5. Are there any limitations to using simple vector difference?

Simple vector difference is limited to situations where the vectors involved have the same number of components and are in the same coordinate system. It also cannot be used to find the difference between non-numeric or non-physical quantities, such as colors or emotions.

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