# Trigonometry : Vectors

## Example Questions

### Example Question #1 : Practical Applications

Determine the magnitude of vector A.

Explanation:

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:

### Example Question #1 : Practical Applications

Which of the following is the correct term for the sum of two vectors?

Sum

Resultant

Velocity

Magnitude

Resultant

Explanation:

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.

### Example Question #3 : Practical Applications

Determine the resultant of  and  .

Explanation:

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.

### Example Question #1 : 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.

Explanation:

To find the resultant we must sum the two vectors:

Now we must graph the resultant

### Example Question #2 : Vectors

How many degrees above the x-axis is ?

Explanation:

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.

### Example Question #1 : Vectors

Find the difference of the two vectors,  which ends at   and  ending at .

-

-

-

Explanation:

When finding the difference of two vectors, you must subtract the x and y components separately.

### Example Question #4 : Vectors

Which of the following is the correct depiction of the difference of vectors A and B?

Explanation:

To find the difference of two vectors we must consider the x and y components separately.

And then we must correctly graph this vector

### Example Question #5 : Vectors

True or False: The magnitude of a vector is the length of the vector.