# Precalculus : Determine if Two Vectors Are Parallel or Perpendicular

## Example Questions

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### Example Question #19 : Matrices And Vectors

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

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

Parallel, because their dot product is one.

Perpendicular, because their dot product is zero.

Perpendicular, because their dot product is one.

Parallel, because their dot product is zero.

Perpendicular, because their dot product is zero.

Explanation:

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 #20 : Matrices And Vectors

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 #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 #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

.

The correct choice is .

### Example Question #5 : 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 #2 : 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 #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

.

Recall that for a vector,

### Example Question #4 : 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 #5 : 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 #6 : 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.

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