In this video,
we're asked to plot or graph the following vectors,
and then we'll also plot a vector
with the initial point not at the origin.
We'll plot these vectors
using the 3D Calc Plotter JavaScript app
from the Exploring Multivariable Calculus site.
Let's open the app and graph these vectors.
When the app is opened,
this is the default surface that is always graphed.
We need to clear this,
and because we are entering vectors,
let's also close this window
by clicking on the X to the right of the equation.
And now to the right of Add to graph,
we click the arrow,
which brings up this drop down menu,
and we select Vector.
And now we enter the components of the first vector here,
and the open angle bracket and close angle bracket
are below the K and L on the keyboard.
The first vector has components
three, comma four, comma zero.
We enter open angle bracket,
three, comma four, comma zero,
close angle bracket.
Let's graph the first vector in blue.
We click color and change our color to blue.
Let's change the width to four
to make the vector easier to see.
And now if we click graph,
the vector appears on the right.
We can also graph the vector
by checking the box to the left of the vector,
which is here.
Looking at the vector,
we need to adjust the window,
which we can do manually here at the bottom,
or we can zoom in or zoom out
using the plus or minus.
Let's zoom out.
Now we have a nice view of this first vector,
and because the Z component is zero,
we can see this first vector is in the X, Y plane.
Let's graph our second vector in red,
which has components three, comma four, comma five.
Click the arrow to the right of add to graph.
Select vector,
and enter the components,
open angle bracket three, comma four, comma five,
close angle bracket.
Let's change the color to red,
width to four,
and click graph.
Notice how the box to the left of the vector is not checked.
Let's go ahead and check it anyway,
and now let's change the orientation
to view these two vectors.
The only difference between these two vectors
is that the red vector has a z-component of five,
and the blue vector has a z-component of zero,
which we should be able to recognize
from the graph of the two vectors.
Let's graph the third vector in green
which has components negative five, comma negative two,
comma negative three.
Click the arrow, select vector,
enter the components, which are again
negative five, comma negative two, comma negative three.
Let's graph this in green.
Change the width to four.
Now if I check the box to the left of the vector,
notice how it graphs the vector as well
or we can click graph.
Let's rotate the view.
Notice for this vector all z-components are negative.
Let's rotate the view to compare the three vectors.
Let's graph the fourth vector in black
which has components
negative four, comma three, comma four.
Click the arrow, select vector,
enter the components,
negative four comma three comma four,
the color is already black, let's change the width to four,
and click graph
or check the box to the left.
The fourth vector is graphed in black.
And let's rotate the view.
Again you may want to pause the video
to make sure you understand
why the vectors are graphed the way that they are.
And our last vector in component form has components
four, comma negative three, comma negative one.
Let's graph this in purple.
Click the arrow, select vector,
enter the components
four comma negative three comma negative one.
Select purple, change the width to four,
again click graph or the box to the left.
Let's rotate the view one last time.
Now all these vectors were in component form
which means the initial points were all at the origin,
zero comma zero comma zero.
For the last part of this question
we're asked to plot the vector with components
six comma negative three comma five
with an initial point
of negative four comma two comma negative three.
Let's finish by graphing this vector in space.
We could clear all these vectors,
let's just uncheck these boxes on the left,
and now we'll add another vector.
We'll click the arrow, select vector,
enter the components of the new vector
which are six comma negative three comma five,
let's graph this vector in orange.
So we'll select orange,
let's change the width to four.
Notice by default, the initial point is the origin
but for this vector the initial point is
negative four comma two comma negative three.
So let's change the initial point.
Notice how the app graphed the vector
with the initial point at the origin.
In order to regraph the vector with this initial point
clicking graph doesn't work
but it does if we click this box to the left.
Notice now the vector is graphed correctly in orange,
the initial point is
negative four comma two comma negative three
and the components are six, comma negative three comma five.
One thing to be aware of is that sometimes
we're asked to graph a vector
when they give us the initial and terminal point
but to graph the vector with this app
we still have to find the component form of the vector
and then enter the component form
as well as the initial point.
And then finally if you want to save any of the graphs
you click the three horizontal bars
in the upper left-hand corner
select File, and select Save the plot as a PNG.
I hope you found this helpful.