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### Course: Algebra (all content)>Unit 19

Lesson 1: Vector basics

# Comparing the components of vectors

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

## Want to join the conversation?

• 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.
• In how do you know at wich point to start at
• You can tell because it is the point... not the arrow. In vectors, direction matters. The point represents the starting point.
• Dear sal sir you have studied us about vectors in this section only graphs but what about their analytical method.
• 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
• What does the triangle mean?
• The triangle is the greek letter delta, it represents change in a quantity. For ex:-
delta x = x final - x initial
• 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.
• 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.

I hoped this helped
• Is a vector made up of the change in x number and the change in y number, so both of them together are called a vector?
Are each components called a vector?
• The components are technically vectors; they have a magnitude and direction.