### All Precalculus Resources

## Example Questions

### Example Question #1 : Determine If Two Vectors Are Parallel Or Perpendicular

Tell whether the following two vectors are perpendicular or parallel and why.

**Possible Answers:**

Parallel, because their dot product is one.

Parallel, because their dot product is zero.

Neither perpendicular nor parallel, because their dot product is neither zero nor one.

Perpendicular, because their dot product is zero.

Perpendicular, because their dot product is one.

**Correct answer:**

Perpendicular, because their dot product is zero.

Two vectors are perpendicular if their dot product is zero, and parallel if their dot product is 1.

Take the dot product of our two vectors to find the answer:

Using our given vectors:

Thus our two vectors are perpendicular.

### Example Question #2 : Determine If Two Vectors Are Parallel Or Perpendicular

Which of the following pairs of vectors are perpendicular?

**Possible Answers:**

**Correct answer:**

Two vectors are perpendicular when their dot product equals to .

Recall how to find the dot product of two vectors and

The correct choice is

### Example Question #3 : Determine If Two Vectors Are Parallel Or Perpendicular

Which of the following pairs of vectors are perpendicular?

**Possible Answers:**

**Correct answer:**

Two vectors are perpendicular when their dot product equals to .

Recall how to find the dot product of two vectors and

.

The correct choice is,

.

### Example Question #4 : Determine If Two Vectors Are Parallel Or Perpendicular

Which of the following pairs of vectors are perpendicular?

**Possible Answers:**

**Correct answer:**

Two vectors are perpendicular when their dot product equals to .

Recall how to find the dot product of two vectors and

.

The correct choice is .

### Example Question #5 : Determine If Two Vectors Are Parallel Or Perpendicular

Which of the following pairs of vectors are perpendicular?

**Possible Answers:**

**Correct answer:**

Two vectors are perpendicular when their dot product equals to .

Recall how to find the dot product of two vectors and

.

Recall that for a vector,

The correct answer is then,

### Example Question #6 : Determine If Two Vectors Are Parallel Or Perpendicular

Which of the following vectors are perpendicular?

**Possible Answers:**

**Correct answer:**

Two vectors are perpendicular when their dot product equals to .

Recall how to find the dot product of two vectors and

.

The correct answer is then,

### Example Question #7 : Determine If Two Vectors Are Parallel Or Perpendicular

Which of the following pairs of vectors are perpendicular?

**Possible Answers:**

**Correct answer:**

Two vectors are perpendicular when their dot product equals to .

Recall how to find the dot product of two vectors and

.

Recall that for a vector,

The correct answer is then,

### Example Question #8 : Determine If Two Vectors Are Parallel Or Perpendicular

Which of the following pairs of vectors are parallel?

**Possible Answers:**

**Correct answer:**

For two vectors, and to be parallel, , for some real number .

The correct answer here is because

.

Therefore,

.

### Example Question #9 : Determine If Two Vectors Are Parallel Or Perpendicular

Which of the following pairs of vectors are parallel?

**Possible Answers:**

**Correct answer:**

For two vectors, and to be parallel, , for some real number .

The correct answer here is because

.

Thus making the vector parallel,

.

### Example Question #10 : Determine If Two Vectors Are Parallel Or Perpendicular

Which of the following pairs of vectors are parallel?

**Possible Answers:**

**Correct answer:**

For two vectors, and to be parallel, , for some real number .

The correct answer here is because

.

Thus making the vector parallel.