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Course: Precalculus>Unit 6

Lesson 2: Vector components

Comparing the components of vectors

Sal figures out which vectors have the same x-component given the graphs of 4 different vectors.

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• Why should vector c be +3? instead of making the black line from (-4,-7) to (-1,-7) if I make the black line from (-1,0) to (-4,0) then I shall get -3 right? Then how can I say if vector c is + or minus 3?
(1 vote)
• The x component is = to the change in x. To get this you take the terminal (end) point and subtract the start point. In the case of vector c we have -1 - -4 = -1+4 = 3.
(3 votes)
• In how do you know at wich point to start at
(4 votes)
• You can tell because it is the point... not the arrow. In vectors, direction matters. The point represents the starting point.
(11 votes)
• Dear sal sir you have studied us about vectors in this section only graphs but what about their analytical method.
(6 votes)
• At the time , Sal said "down by three (3)." Did he mean " to the left three? Just wanted to make it clear because i got confused
(4 votes)
• In how do you know at wich point to start at
(1 vote)
• Look at the point with the v-shape. That tells you the end point of the vector or the terminating point. Follow the components in reverse to find the initial point. That's how you know at which point to start.
(4 votes)
• how can I solve a vector as a word problem?
For example: a 200-pound cart sits on a ramp inclined at 30 degrees. What force is required to keep the cart from rolling down the ramp?
I know that the solution is 100 pounds, but I'm not sure how to approach that answer using trig.
(1 vote)
• When I see this kind of problem, a good start is to draw the diagram with the forces at play, since this looks like a physics problem. There is the gravitational force (Fg), the normal force (Fn), and the applied force (Fa) to keep the cart in place. Friction can't be calculated from the given information so it's assumed to be a frictionless plane.

Fg is 200 pounds and points downward from the cart, so the other two forces must cancel it out. Fn is always perpendicular to the surface while Fa is parallel to the incline. The 3 vectors then form a triangle with Fg as the hypotenuse because Fn and Fa must form the opposing force that cancels Fg. You should be able to find that the angle between Fg and Fn is 30 using right triangles. Then you can apply trig and find out that Fa is 100 pounds (200sin(30) = 100). Fn = 200cos(30)= 173.2050808...

If my explanation didn't make sense (it is pretty bad) then go to khan academy's section on physics.
https://www.khanacademy.org/science/physics/forces-newtons-laws#inclined-planes-friction

I hoped this helped
(4 votes)
• how do you know which direction to go?
(1 vote)
• You look at the starting and ending point to determine the direction of the vector. That means, you look for an arrow in the line, which shows you the 'head' and 'tail'. The front of the arrow is the end point, also known as the terminal point, while the back of the arrow is the start point, the initial point. Then, you look for the x and y changes needed to go from the initial TO the terminal point.

For example, if you have an initial point of (0, 0) and a terminal point of (1, 1) then the arrow will point toward the point (1,1) and we know that the horizontal and vertical [x and y] 'movements' have a size of, a magnitude of one.
(3 votes)
• Is it like getting the slope of a linear function?
(0 votes)
• Well, yes but actually no...

It's more like determining the change in the x-axis, then the change in the y-axis and plugging in those values in this bracket: ( ▲x , ▲y ).
(3 votes)
• Does it make any difference where you start the vector as long as you maintain its magnitude and direction?
(1 vote)
• The start of the vector doesn't really matter but sometimes it can be useful so don't change it just in case.
(1 vote)
• How do vectors and scalars differ from each other?
(1 vote)
• Vectors have a magnitude and a direction.
Scalars do not have directions, only magnitudes.
(1 vote)

Video transcript

- We're asked, "Which of the following vectors have "the same x component as vector a?" And they tell us to "Select all that apply" This is vector a right over here and we only have to concern ourselves with the x component. That's what they're asking us about. Let's think about what it's x component is. We're starting at this point right over here, which has an x value of negative two and we're going from x equals negative two to x is equal to negative five. Our change in x, another way to think about it, our x component. We're going from negative two to negative five. Our x value goes down by three. Our change in x is equal to negative three. That would also be the x component of vector a. We could say that vector a is equal to, it's x component is negative three. We're not concerning ourselves with our y component but we see that our y goes up by one. So it's negative three comma one but we just care about our x component. Let's think about what other vectors here have an x component of negative three. That, if we start at our initial point and go to the terminal point, our x value has gone down by three. We're gonna start with vector b here. And let's see, if we start there our x value is three at our initial point, our starting point for that vector. Then, to go to the x value of the terminal point we once again went down by three. This has the same x component. Vector b is going to be negative three comma something. I will select that one. Let's think about vector c. Vector c starts here at x equals negative 4 and then it ends at x equals negative one. It's x component is going to look, one way to think about it, our change in x is going to look like this. You might be tempted to say this is the same thing. It has a length of three but notice, we're not going three to the left, the way that we did in vector a or in vector b. We're going three to the right. Here our change in x is positive three and so vector c is going to be positive three comma something. It's not gonna be vector c. Now let's look at vector d. Vector d starts over here, it's x value is negative six and we're going from x equals negative six to x equals negative nine. Once again we have gone down. Our change in x is negative three. That has the same x component. If I were to say vector d I would say it's negative three comma something. I haven't figured out what these are but I don't need to for this problem. So vector d also has the same x component, an x component of negative three and we're done.