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### Course: Get ready for AP® Calculus>Unit 8

Lesson 3: Vector components

# Finding the components of a vector

Sal finds the x and y-components of a vector given its graph.

## Want to join the conversation?

• Why did he start from A (4,4) instead of B (-7,-8)
• Remember, in a vector, there is a specific beginning and ending point, and the ending point is marked as an arrow. The reason an arrow is used is because a vector uses magnitude, the amount something moves, or the speed with which it moves, and direction. In this case, the direction is left and down. Does that help? I hope it did.
• When it comes to solving vector components, I am still confused when to add or subtract the points.
• You ALWAYS subtract the points. The thing is you subtract ENDING POINT - STARTING POINT. The problem you're given will define the direction of the vector. So, if the direction defined by the problem is "A to B", you subtract Point B - Point A. If the direction is defined by the problem as "B to A", you subtract Point A - Point B.
• I've seen any questions of this kind that don't provide graphs like this. So if we are to find components like that of the first question in the video without the graph, how do you do it?
• All you really need are the points. From there you find your change in x and change in y through subtraction or construction of your own graph.
• What's the point of knowing the components? Does it help in determining if two points have the same direction?
• Yep, you use the components and trigonometry to determine the angle of the vector, and that tells you the direction
(1 vote)
• but why did we go in that specific direction? can we not go in the other direction and get different values for the components? and does this mean that change in x and change in y are the components?
• You could go down from point A and go left to reach point B (if that's what you meant by "other direction"). But, observe that the vectors you get will still be the same and hence, a vector cannot have two sets of components if taken in two different directions.

Change in x and change in y are indeed the components. They cumulatively make up the change in position from A to B, which is exactly what the vector is showing us here.
• How do you know what direction to move the arrows, right or left? It depends on what?
• There are two hints here as to the direction of the vector AB:
1) The arrow over the top of AB indicates that the vector starts at A and terminates at B; and 2) If you look at the diagram, it'll show that the arrow does, in fact, "point" toward the point B.
• In my Trigonometry class, my teacher specifically said to use Chevron brackets, which are ⟨ ⟩, when writing component form. Shouldn't the vector be ⟨-11,-12⟩ instead of (-11,-12)?
(1 vote)
• That is an effective way to show that you are talking about a vector and not an ordered pair, but its more a matter of choice than a mathematic rule. Plus, every point on a graph can be described as the terminal end of a position vector, so an ordered pair can be thought of as the end of a vector.
I wouldn't worry too much about it. Just follow the rules in your classes, but remember that some of them aren't universal.
• So I got this question asking: Vector AB has a terminal point (4,-7), an x component of -3 and a y component of -9. FIND THE COORDINATES OF IT'S INITIAL POINT. Is there a video on questions like this.
(1 vote)
• A vector is equal to its terminal point minus its initial point. Therefore, we have
(-3, -9) = (4, -7) - initial point
initial point = (4, -7) - (-3, -9) = (4 - (-3), -7 - (-9)) = (7, 2).
The initial point is (7, 2).

Have a blessed, wonderful day!