Precalculus : Determine if Two Vectors Are Parallel or Perpendicular

Study concepts, example questions & explanations for Precalculus

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Example Questions

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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 zero.

Perpendicular, because their dot product is one.

Parallel, because their dot product is one.

Perpendicular, because their dot product is zero.

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

Correct answer:

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 #17 : Matrices And Vectors

Which of the following pairs of vectors are perpendicular?

Possible Answers:

Correct answer:

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?

Possible Answers:

Correct answer:

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?

Possible Answers:

Correct answer:

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?

Possible Answers:

Correct answer:

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, 

The correct answer is then,

 

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

Which of the following vectors are perpendicular?

Possible Answers:

Correct answer:

Explanation:

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 #3 : Determine If Two Vectors Are Parallel Or Perpendicular

Which of the following pairs of vectors are perpendicular?

Possible Answers:

Correct answer:

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, 

The correct answer is then,

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

Which of the following pairs of vectors are parallel?

Possible Answers:

Correct answer:

Explanation:

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

The correct answer here is  because

.

Therefore,

.

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

Which of the following pairs of vectors are parallel?

Possible Answers:

Correct answer:

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 #4 : Determine If Two Vectors Are Parallel Or Perpendicular

Which of the following pairs of vectors are parallel?

Possible Answers:

Correct answer:

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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