Vectors - Trigonometry
Card 0 of 32
Determine the magnitude of vector A.

Determine the magnitude of vector A.
We can use the pythagorean theorem to solve this problem. Using
as our hypotenuse, we can drop a vertical vector perpendicular to the x-axis. We will call this
and it is 4 units in length. We can also extend a vector from the origin that connects to
. We will call this
and it is 3 units in length.

Using the pythagorean theorem:






We can use the pythagorean theorem to solve this problem. Using as our hypotenuse, we can drop a vertical vector perpendicular to the x-axis. We will call this
and it is 4 units in length. We can also extend a vector from the origin that connects to
. We will call this
and it is 3 units in length.
Using the pythagorean theorem:
Compare your answer with the correct one above
Which of the following is the correct term for the sum of two vectors?
Which of the following is the correct term for the sum of two vectors?
When summing two vectors, you have both an x and y component and you sum these separately leaving you with a coordinate as your answer. This coordinate is called a resultant.
When summing two vectors, you have both an x and y component and you sum these separately leaving you with a coordinate as your answer. This coordinate is called a resultant.
Compare your answer with the correct one above
Determine the resultant of
and
.
Determine the resultant of and
.
When determining the resultant of two vectors, you are finding the sum of two vectors. To do this you must add the x component and the y component separately.



When determining the resultant of two vectors, you are finding the sum of two vectors. To do this you must add the x component and the y component separately.
Compare your answer with the correct one above
Consider the following graphs where
begins at the origin and ends at
and
. Which of the following depicts the correct resultant of these two vectors.

Consider the following graphs where begins at the origin and ends at
and
. Which of the following depicts the correct resultant of these two vectors.
To find the resultant we must sum the two vectors:



Now we must graph the resultant

To find the resultant we must sum the two vectors:
Now we must graph the resultant
Compare your answer with the correct one above
How many degrees above the x-axis is
?

How many degrees above the x-axis is ?
First, we must understand what we are solving for. We are solving for the angle that is formed by
and the x-axis. To do this, we can extend a vector from the origin which stops directly under the end of
. We will call this new vector
and it will be 7 units long. We will also extend a vector upwards that is perpendicular to the x-axis. We will call this
and it will be 3 units long.

Now we can use the relationship that
where
is the adjacent side and
is the opposite side.




And so
is 23.2 degrees above the x-axis.
First, we must understand what we are solving for. We are solving for the angle that is formed by and the x-axis. To do this, we can extend a vector from the origin which stops directly under the end of
. We will call this new vector
and it will be 7 units long. We will also extend a vector upwards that is perpendicular to the x-axis. We will call this
and it will be 3 units long.
Now we can use the relationship that where
is the adjacent side and
is the opposite side.
And so is 23.2 degrees above the x-axis.
Compare your answer with the correct one above
Find the difference of the two vectors,
which ends at
and
ending at
.
Find the difference of the two vectors, which ends at
and
ending at
.
When finding the difference of two vectors, you must subtract the x and y components separately.



When finding the difference of two vectors, you must subtract the x and y components separately.
Compare your answer with the correct one above
Which of the following is the correct depiction of the difference of vectors A and B?

Which of the following is the correct depiction of the difference of vectors A and B?
To find the difference of two vectors we must consider the x and y components separately.



And then we must correctly graph this vector

To find the difference of two vectors we must consider the x and y components separately.
And then we must correctly graph this vector
Compare your answer with the correct one above
True or False: The magnitude of a vector is the length of the vector.
True or False: The magnitude of a vector is the length of the vector.
When finding the magnitude of the vector, you use either the Pythagorean Theorem by forming a right triangle with the vector in question or you can use the distance formula. This is much more clear considering the distance vector that the magnitude of the vector is in fact the length of the vector.
When finding the magnitude of the vector, you use either the Pythagorean Theorem by forming a right triangle with the vector in question or you can use the distance formula. This is much more clear considering the distance vector that the magnitude of the vector is in fact the length of the vector.
Compare your answer with the correct one above
Determine the magnitude of vector A.

Determine the magnitude of vector A.
We can use the pythagorean theorem to solve this problem. Using
as our hypotenuse, we can drop a vertical vector perpendicular to the x-axis. We will call this
and it is 4 units in length. We can also extend a vector from the origin that connects to
. We will call this
and it is 3 units in length.

Using the pythagorean theorem:






We can use the pythagorean theorem to solve this problem. Using as our hypotenuse, we can drop a vertical vector perpendicular to the x-axis. We will call this
and it is 4 units in length. We can also extend a vector from the origin that connects to
. We will call this
and it is 3 units in length.
Using the pythagorean theorem:
Compare your answer with the correct one above
Which of the following is the correct term for the sum of two vectors?
Which of the following is the correct term for the sum of two vectors?
When summing two vectors, you have both an x and y component and you sum these separately leaving you with a coordinate as your answer. This coordinate is called a resultant.
When summing two vectors, you have both an x and y component and you sum these separately leaving you with a coordinate as your answer. This coordinate is called a resultant.
Compare your answer with the correct one above
Determine the resultant of
and
.
Determine the resultant of and
.
When determining the resultant of two vectors, you are finding the sum of two vectors. To do this you must add the x component and the y component separately.



When determining the resultant of two vectors, you are finding the sum of two vectors. To do this you must add the x component and the y component separately.
Compare your answer with the correct one above
Consider the following graphs where
begins at the origin and ends at
and
. Which of the following depicts the correct resultant of these two vectors.

Consider the following graphs where begins at the origin and ends at
and
. Which of the following depicts the correct resultant of these two vectors.
To find the resultant we must sum the two vectors:



Now we must graph the resultant

To find the resultant we must sum the two vectors:
Now we must graph the resultant
Compare your answer with the correct one above
How many degrees above the x-axis is
?

How many degrees above the x-axis is ?
First, we must understand what we are solving for. We are solving for the angle that is formed by
and the x-axis. To do this, we can extend a vector from the origin which stops directly under the end of
. We will call this new vector
and it will be 7 units long. We will also extend a vector upwards that is perpendicular to the x-axis. We will call this
and it will be 3 units long.

Now we can use the relationship that
where
is the adjacent side and
is the opposite side.




And so
is 23.2 degrees above the x-axis.
First, we must understand what we are solving for. We are solving for the angle that is formed by and the x-axis. To do this, we can extend a vector from the origin which stops directly under the end of
. We will call this new vector
and it will be 7 units long. We will also extend a vector upwards that is perpendicular to the x-axis. We will call this
and it will be 3 units long.
Now we can use the relationship that where
is the adjacent side and
is the opposite side.
And so is 23.2 degrees above the x-axis.
Compare your answer with the correct one above
Find the difference of the two vectors,
which ends at
and
ending at
.
Find the difference of the two vectors, which ends at
and
ending at
.
When finding the difference of two vectors, you must subtract the x and y components separately.



When finding the difference of two vectors, you must subtract the x and y components separately.
Compare your answer with the correct one above
Which of the following is the correct depiction of the difference of vectors A and B?

Which of the following is the correct depiction of the difference of vectors A and B?
To find the difference of two vectors we must consider the x and y components separately.



And then we must correctly graph this vector

To find the difference of two vectors we must consider the x and y components separately.
And then we must correctly graph this vector
Compare your answer with the correct one above
True or False: The magnitude of a vector is the length of the vector.
True or False: The magnitude of a vector is the length of the vector.
When finding the magnitude of the vector, you use either the Pythagorean Theorem by forming a right triangle with the vector in question or you can use the distance formula. This is much more clear considering the distance vector that the magnitude of the vector is in fact the length of the vector.
When finding the magnitude of the vector, you use either the Pythagorean Theorem by forming a right triangle with the vector in question or you can use the distance formula. This is much more clear considering the distance vector that the magnitude of the vector is in fact the length of the vector.
Compare your answer with the correct one above
Determine the magnitude of vector A.

Determine the magnitude of vector A.
We can use the pythagorean theorem to solve this problem. Using
as our hypotenuse, we can drop a vertical vector perpendicular to the x-axis. We will call this
and it is 4 units in length. We can also extend a vector from the origin that connects to
. We will call this
and it is 3 units in length.

Using the pythagorean theorem:






We can use the pythagorean theorem to solve this problem. Using as our hypotenuse, we can drop a vertical vector perpendicular to the x-axis. We will call this
and it is 4 units in length. We can also extend a vector from the origin that connects to
. We will call this
and it is 3 units in length.
Using the pythagorean theorem:
Compare your answer with the correct one above
Which of the following is the correct term for the sum of two vectors?
Which of the following is the correct term for the sum of two vectors?
When summing two vectors, you have both an x and y component and you sum these separately leaving you with a coordinate as your answer. This coordinate is called a resultant.
When summing two vectors, you have both an x and y component and you sum these separately leaving you with a coordinate as your answer. This coordinate is called a resultant.
Compare your answer with the correct one above
Determine the resultant of
and
.
Determine the resultant of and
.
When determining the resultant of two vectors, you are finding the sum of two vectors. To do this you must add the x component and the y component separately.



When determining the resultant of two vectors, you are finding the sum of two vectors. To do this you must add the x component and the y component separately.
Compare your answer with the correct one above
Consider the following graphs where
begins at the origin and ends at
and
. Which of the following depicts the correct resultant of these two vectors.

Consider the following graphs where begins at the origin and ends at
and
. Which of the following depicts the correct resultant of these two vectors.
To find the resultant we must sum the two vectors:



Now we must graph the resultant

To find the resultant we must sum the two vectors:
Now we must graph the resultant
Compare your answer with the correct one above