Precalculus : Matrices and Vectors

Study concepts, example questions & explanations for Precalculus

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Example Questions

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 

.

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:

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?

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 #1 : 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 #7 : 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 #8 : 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 #9 : 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 #10 : 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 #11 : 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 

Making the vector parallel as follows.

Example Question #11 : 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 .

Recall that for a vector, .

The correct answer here is 

This is the correct answer because .

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