### All Precalculus Resources

## Example Questions

### Example Question #1 : Find The Sum And Difference Of Vectors

Evaluate

**Possible Answers:**

None of the other answers

**Correct answer:**

When adding two vectors, they need to be expanded into their components. Luckily, the problem statement gives us the vectors already in their component form. From here, we just need to remember that we can only add like components. So for this problem we get:

Now we can combine those values to write out the complete vector:

### Example Question #2 : Find The Sum And Difference Of Vectors

What is the magnitude and angle for the following vector, measured CCW from the x-axis?

**Possible Answers:**

**Correct answer:**

The magnitude of the vector is found using the distance formula:

To calculate the angle we must first find the inverse tangent of :

This angle value is the principal arctan, but it is in the fourth quadrant while our vector is in the second. We must add the angle 180° to this value to arrive at our final answer.

### Example Question #3 : Find The Sum And Difference Of Vectors

Vector has a magnitude of 3.61 and a direction 124° CCW from the x-axis. Express in unit vector form.

**Possible Answers:**

**Correct answer:**

### Example Question #4 : Find The Sum And Difference Of Vectors

What are the magnitude and angle, CCW from the x-axis, of ?

**Possible Answers:**

**Correct answer:**

When multiplying a vector by a constant (called scalar multiplication), we multiply each component by the constant.

The magnitude of this new vector is found with these new components:

To calculate the angle we must first find the inverse tangent of :

This is the principal arctan, but it is in the first quadrant while our vector is in the third. We to add the angle 180° to this value to arrive at our final answer.

### Example Question #5 : Find The Sum And Difference Of Vectors

Vector has a magnitude of 2.24 and is at an angle of 63.4° CCW from the x-axis. Vector has a magnitude of 3.16 at an angle of 342° CCW from the x-axis.

Find by using the nose-to-tail graphical method.

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### Example Question #6 : Find The Sum And Difference Of Vectors

Find the magnitude and angle CCW from the x-axis of using the nose-to-tail graphical method.

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### Example Question #7 : Find The Sum And Difference Of Vectors

Express a vector with magnitude 2.24 directed 63.4° CCW from the x-axis in unit vector form.

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### Example Question #8 : Find The Sum And Difference Of Vectors

Vector has a magnitude of 2.24 and is at an angle of 63.4° CCW from the x-axis. Vector has a magnitude of 3.61 and is at an angle of 124° CCW from the x-axis.

Find by using the nose-to-tail graphical method.

**Possible Answers:**

**Correct answer:**

First, construct the two vectors using ruler and protractor:

is twice the length of , but in the same direction:

Since we are subtracting, reverse the direction of :

Form by placing the tail of at the nose of :

Construct and measure the resultant from the tail of to the nose of with a ruler and protractor.

### Example Question #9 : Find The Sum And Difference Of Vectors

Vector has a magnitude of 2.24 and is at an angle of 63.4° CCW from the x-axis. Vector has a magnitude of 3.16 at an anlge of 342° CCW from the x-axis.

Find by using the parallelogram graphical method.

**Possible Answers:**

### Example Question #10 : Find The Sum And Difference Of Vectors

Find using the parallelogram graphical method.

**Possible Answers:**

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