This video is about X and Y components of vectors. All vectors have what's called an X component and
a Y component. So this is vector A. I'm going to be using this as an example. The X component is
how far in the horizontal direction the vector travels. So if this is vector A,
this is its X component right here. And its Y component is how far in the vertical direction
the vector travels. So that would be the Y component of vector A. That's how far in the
up-down direction it goes. So we call these X and Y components because they go along the
X and Y axes of a graph. So we can have X components and we can have Y components,
and that really just means that they're pointing along the X or Y axis. X and Y components are
themselves vectors. They also have directions. like a vector A is going up into the right so
its X component points to the right and it's Y component points up and we have this special
label for vectors that are X and Y components of other vectors. If the original vector is A the X
component of A will be A-X and the Y component will be A-Y so we could draw these like this.
Just as a real-world example, we could imagine a bird flying up in a certain direction,
and the vector of the bird's motion I'm going to call it vector A, the X component of the bird's
motion Ax could be thought of as how far along the ground the bird shadow traveled as it moved,
and the Y component of the bird's motion would be how high into the air the bird went, so X
and Y components can have real physical meanings in addition to the original vector that they're
making up. Even if you have a perfectly horizontal or perfectly vertical vector we can still say that
it technically has an X and Y component. The X component is how far it goes in the horizontal
direction, and so if this is 5 meters perfectly horizontally that means the X component is just
5 meters. It's the same as the original vector, and we would just say that the Y component is 0
here because it's not going up or down at all. So this would be like the bird moving 5 meters along
the ground. If we were to ask for its X component we would be really asking for how far its shadow
moved along the ground, which we know would be 5 meters, and if we asked for its Y component
we'd really be asking how high into the air did it go? And we know that that would be 0 meters.
There are two general rules for X and Y components and how they relate to a vector. You can see first
of all that they actually obey the rules of vector addition (the tip to tail method) and the
X component plus the Y component as vectors, if we're adding them using vector math rather than
regular math, the tip to tail method means that the x and y components always add together to be the
original vector. So a vector is equal to the sum of its x and y components. So that's the first rule.
You'll also notice that no matter how we draw the X component and no matter how we draw the
Y component they're always going to form a right triangle with the original vector. So as another
example, if we have this vector here and this is its X component and this is its Y component we
can see that when we put them together in vector addition they're equal to the original vector.
So that will always be true. One common mistake with this rule is that students sometimes assume that
the numbers themselves add up to be the total of the vector, so if we imagine that the X component
is 3 and the Y is 4 that overall vector using the Pythagorean theorem will be 5, it won't be 7, so
it's not that the scalars add together, it's that the vectors using vector addition add together. To
make that total vector so I can see here that the scalar quantities look like this, which means that this rule does not work for scalars it only works
when you're using the full vector and the tip to
tail method to find the answer. So just adding the scalars together won't work. You may have noticed
however that no matter how we draw vectors, their X and Y-components always form perfect right
triangles with them when we draw them, because the X and Y components are by definition at 90-degree
angles to each other. So because of the Pythagorean theorem that means that the X and Y components
will always be related to the full vector. Using the Pythagorean Theorem A^2 + B^2
= C^2, so this WILL always be true, and if I rearrange this into a general rule the total
vector is going to be equal to the square root of the squares of its own X and Y component if
I draw it as a scalar rather than a vector like this. So if we just focus on the scalar
quantities this will always be true for the X and Y components of a vector. This is just
a summary of what we've talked about. And that's what you need to know about X and y components.