# Calculus 3 : Vector Subtraction

## Example Questions

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### Example Question #1 : Vector Subtraction

Find the difference

Explanation:

The difference  of two vectors  and  is defined as

For the two vectors

The difference is

### Example Question #2 : Vector Subtraction

Given the vectors

find .

Explanation:

Given the vectors

we can find the difference by subtracting component-wise

### Example Question #3 : Vector Subtraction

Perform the following operation on the vectors specified below:

Where

Explanation:

First, multiply out the vectors by their corresponding coefficients:

Now we simply subtract the two vectors:

### Example Question #4 : Vector Subtraction

Subtract the vectors  and

Explanation:

Set up an expression to subtract the vectors.

Be sure to make note of the sign change when subtracting the vectors.

Simplify the vector.

### Example Question #5 : Vector Subtraction

Find the difference, , of the two vectors.

Explanation:

To find the difference, , we distribute the minus sign and turn it into vector addition.

The sum of two vectors is defined as

The sum of two vectors

is defined as

As such, the difference is

### Example Question #1 : Vector Subtraction

Compute the following: .

Explanation:

The formula for subtracting vectors is . Plugging in the values we were given, we get

### Example Question #2 : Vector Subtraction

Solve:

Explanation:

To subtract vectors, we simply subtract their respective components:

Note that our result is a vector still.

### Example Question #8 : Vector Subtraction

Find the difference between  and .

Explanation:

The formula for the difference of vectors is

Using the vectors given, we get

.

### Example Question #3 : Vector Subtraction

Compute the following operation: .

Explanation:

The formula for subtracting vectors a and b is

.

Plugging in the values we were given, we get

### Example Question #10 : Vector Subtraction

Perform the following vector operation: