Calculus 3 : Normal Vectors

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #41 : Normal Vectors

Determine whether the two vectors,  and , are orthogonal or not.

Possible Answers:

The two vectors are orthogonal.

The two vectors are not orthogonal.

Correct answer:

The two vectors are not orthogonal.

Explanation:

Vectors can be said to be orthogonal, that is to say perpendicular or normal, if their dot product amounts to zero:

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors,  and 

The two vectors are not orthogonal. It may be observed that since these nontrivial vectors are identical, they could not be perpendicular.

Example Question #42 : Normal Vectors

Determine whether the two vectors,  and , are orthogonal or not.

Possible Answers:

The two vectors are orthogonal.

The two vectors are not orthogonal.

Correct answer:

The two vectors are orthogonal.

Explanation:

Vectors can be said to be orthogonal, that is to say perpendicular or normal, if their dot product amounts to zero:

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors,  and 

The two vectors are orthogonal.

Example Question #43 : Normal Vectors

Determine whether the two vectors,  and , are orthogonal or not.

Possible Answers:

The two vectors are orthogonal.

The two vectors are not orthogonal.

Correct answer:

The two vectors are not orthogonal.

Explanation:

Vectors can be said to be orthogonal, that is to say perpendicular or normal, if their dot product amounts to zero:

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors,  and 

The two vectors are not orthogonal.

Example Question #44 : Normal Vectors

Determine whether the two vectors,  and , are orthogonal or not.

Possible Answers:

The two vectors are not orthogonal.

The two vectors are orthogonal.

Correct answer:

The two vectors are orthogonal.

Explanation:

Vectors can be said to be orthogonal, that is to say perpendicular or normal, if their dot product amounts to zero:

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors,  and 

The two vectors are orthogonal.

Example Question #45 : Normal Vectors

Determine whether the two vectors,  and , are orthogonal or not.

Possible Answers:

The two vectors are not orthogonal.

The two vectors are orthogonal.

Correct answer:

The two vectors are orthogonal.

Explanation:

Vectors can be said to be orthogonal, that is to say perpendicular or normal, if their dot product amounts to zero:

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors,  and 

The two vectors are orthogonal.

Example Question #46 : Normal Vectors

Determine whether the two vectors,  and , are orthogonal or not.

Possible Answers:

The two vectors are not orthogonal.

The two vectors are orthogonal.

Correct answer:

The two vectors are orthogonal.

Explanation:

Vectors can be said to be orthogonal, that is to say perpendicular or normal, if their dot product amounts to zero:

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors,  and 

The two vectors are orthogonal.

Example Question #47 : Normal Vectors

Determine whether the two vectors,  and , are orthogonal or not.

Possible Answers:

The two vectors are orthogonal.

The two vectors are not orthogonal.

Correct answer:

The two vectors are orthogonal.

Explanation:

Vectors can be said to be orthogonal, that is to say perpendicular or normal, if their dot product amounts to zero:

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors,  and 

The two vectors are orthogonal.

Example Question #48 : Normal Vectors

Determine whether the two vectors,  and , are orthogonal or not.

Possible Answers:

The two vectors are orthogonal.

The two vectors are not orthogonal.

Correct answer:

The two vectors are not orthogonal.

Explanation:

Vectors can be said to be orthogonal, that is to say perpendicular or normal, if their dot product amounts to zero:

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors,  and 

The two vectors are not orthogonal.

Example Question #49 : Normal Vectors

Determine whether the two vectors,  and , are orthogonal or not.

Possible Answers:

The two vectors are orthogonal.

The two vectors are not orthogonal.

Correct answer:

The two vectors are not orthogonal.

Explanation:

Vectors can be said to be orthogonal, that is to say perpendicular or normal, if their dot product amounts to zero:

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors,  and 

The two vectors are not orthogonal.

Example Question #50 : Normal Vectors

Determine whether the two vectors,  and , are orthogonal or not.

Possible Answers:

The two vectors are orthogonal.

The two vectors are not orthogonal.

Correct answer:

The two vectors are not orthogonal.

Explanation:

Vectors can be said to be orthogonal, that is to say perpendicular or normal, if their dot product amounts to zero:

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors,  and 

The two vectors are not orthogonal.

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