# Precalculus : Matrices and Vectors

## Example Questions

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

Which of the following pairs of vectors are perpendicular?

Explanation:

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 #2 : Determine If Two Vectors Are Parallel Or Perpendicular

Which of the following pairs of vectors are perpendicular?

Explanation:

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?

Explanation:

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?

Explanation:

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,

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

Which of the following vectors are perpendicular?

Explanation:

Two vectors are perpendicular when their dot product equals to .

Recall how to find the dot product of two vectors  and

.

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

Which of the following pairs of vectors are perpendicular?

Explanation:

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,

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

Which of the following pairs of vectors are parallel?

Explanation:

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

The correct answer here is  because

.

Therefore,

.

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

Which of the following pairs of vectors are parallel?

Explanation:

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

The correct answer here is  because

.

Thus making the vector parallel,

.

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

Which of the following pairs of vectors are parallel?

Explanation:

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?