I totally don't understand Vectors
How do you describe a vector as an ordered pair?
on the x and Y where they cross it is 41 degrees and goes to the left up to the y 77
I am totally confused Help
There are two common ways to describe a point in the plane.
Most familiar is the rectangular coordinates (x,y) which says how far left-right or up-down the point is from the origin (0,0).
Another way is to specify how far away a point is from the pole (0,0), and in which direction θ. The direction is usually expressed as 0-360° when first learning about polar coordinates.
So, you need to get familiar with the circle and how to handle degrees.
An (x,y) pair can be determined from an (r,θ) pair by referring to the right triangle with the vector to the point as hypotenuse.
x = r cosθ
y = r sinθ
to go the other way,
tanθ = y/x
r2 = x2 + y2
If all this looks unfamiliar, you need to check your textbook and have a one-on-one session with someone in person.
It sounds like your question is referring to a point where
θ = 41°
r = 77
To get the (x,y) coordinates,
x = 77 cos 41° = 58.1
y = 77 sin 41° = 50.5
Don't worry, I'm here to help unravel the mystery of vectors with a touch of humor!
Describing a vector as an ordered pair can be as simple as having a two-item to-do list. In our case, the ordered pair consists of an x-component and a y-component.
Now, let's tackle your specific example. You mentioned that the vector is at 41 degrees where the x and y-axis cross, and it goes to the left and up to the y-value of 77. Let's break it down:
The x-component represents the leftward or rightward movement. Since the vector goes to the left, we can think of it having a negative x-component. But hold up, the angle is at the intersection of the x and y-axis, which means the x-component is the one affected. So, we have a negative x-component in this case.
The y-component represents the upward or downward movement. The vector goes up to the y-value of 77, so we can deduce that the y-component is positive.
Putting it all together, our vector, as an ordered pair, would be (-x-component, y-component). In this case, based on the information you provided, the vector can be described as (-?, 77). To determine the exact numerical values, we'll need more information to calculate the lengths of the components.
Hopefully, this explanation brought a smile to your face while demystifying vectors a bit! Feel free to ask more questions or provide additional details for a more accurate description.
To describe a vector as an ordered pair, you can use the coordinates of its endpoint. In your case, if the vector starts at the origin (or any other reference point) and ends at the point (x, y), you would describe the vector as (x, y).
Now let's apply this to your specific example. You mentioned that the vector starts from the point where the x and y axes intersect and goes to the left and up. You also specified that the angle between the vector and the positive x-axis is 41 degrees. The length of the vector is not provided, so we can assume it to be arbitrary for now.
To describe this vector as an ordered pair, we need to determine its endpoint coordinates. To do that, we can use trigonometry. Since the vector makes an angle of 41 degrees with the positive x-axis, we can use the given angle and the lengths of the sides of a right triangle to determine the x and y components of the vector.
Let's assign lengths to the sides of the triangle. Let the hypotenuse represent the length of the vector (which is arbitrary), the side adjacent to the angle of 41 degrees be the x-component, and the side opposite the angle be the y-component. To find the x and y components, we can use the following trigonometric formulas:
x = hypotenuse * cos(angle)
y = hypotenuse * sin(angle)
Now, substituting the given values into the formulas, we have:
x = hypotenuse * cos(41 degrees)
y = hypotenuse * sin(41 degrees)
Since the length of the vector (hypotenuse) is not specified, we won't be able to provide specific values for x and y. However, this formula will give you the general form for expressing the vector as an ordered pair.
No problem! I can help explain vectors to you.
A vector is a mathematical quantity that has both magnitude (or length) and direction. It is often represented as an arrow.
To describe a vector as an ordered pair, we typically use a coordinate system with two axes: the x-axis and the y-axis.
In your case, you mentioned that the vector starts at the point where the x and y axes cross, which is the origin (0,0). You also mentioned that the angle between the vector and the x-axis is 41 degrees, and it goes to the left and up to the y-axis at a length of 77 units.
Here's how you can describe this vector as an ordered pair:
1. Determine the x-component: To find the x-component of the vector, you can use trigonometry. Since the angle between the vector and the x-axis is 41 degrees, you can use the cosine function to find the x-component. The formula is:
x-component = magnitude * cosine(angle)
In this case, the magnitude is 77 and the angle is 41 degrees. Using this information, you can calculate the x-component.
2. Determine the y-component: Similarly, to find the y-component of the vector, you can use the sine function. The formula is:
y-component = magnitude * sine(angle)
In this case, the magnitude is 77 and the angle is 41 degrees. Using this information, you can calculate the y-component.
3. Write the ordered pair: Once you have calculated the x-component and y-component, you can write them as an ordered pair (x, y). The x-value represents the horizontal displacement and the y-value represents the vertical displacement.
So, to describe your vector as an ordered pair, you can calculate the x-component and y-component using the formulas above, and then write it as (x, y).
I hope this explanation helps! Let me know if you have any further questions.