Calculus 3 : Normal Vectors

Study concepts, example questions & explanations for Calculus 3

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Example Questions

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Example Question #91 : Normal Vectors

Find the normal vector to the plane containing the vectors  and 

Possible Answers:

Correct answer:

Explanation:

To find the normal vector to a plane containing vectors  and , you take the cross product of the two vectors. 

To find the cross product between the two vectors  and , you take the determinant of the 3x3 matrix 

Using the vectors from the problem statement, we get

Example Question #92 : Normal Vectors

Find the normal vector to the plane containing the vectors  and 

Possible Answers:

Correct answer:

Explanation:

To obtain the normal vector to a plane containing two vectors  and , you compute the determinant of the 3x3 matrix 

Using this formula, we evaluate using the vectors from the problem statement:

Example Question #93 : Normal Vectors

Find the normal vector to the plane that contains the vectors  and 

Possible Answers:

Correct answer:

Explanation:

To obtain the normal vector to a plane containing two vectors  and , you compute the determinant of the 3x3 matrix 

Using this formula, we evaluate using the vectors from the problem statement:

Example Question #94 : Normal Vectors

Find the normal vector to the plane that contains the vectors  and 

Possible Answers:

Correct answer:

Explanation:

To obtain the normal vector to a plane containing two vectors  and , you compute the determinant of the 3x3 matrix 

Using this formula, we evaluate using the vectors from the problem statement:

Example Question #95 : Normal Vectors

Find the normal vector to the plane that contains the vectors  and 

Possible Answers:

Correct answer:

Explanation:

To obtain the normal vector to a plane containing two vectors  and , you compute the determinant of the 3x3 matrix 

Using this formula, we evaluate using the vectors from the problem statement:

Example Question #96 : Normal Vectors

Find the Unit Normal Vector to the given plane. 

.

Possible Answers:

Correct answer:

Explanation:

Recall the definition of the Unit Normal Vector.

Let 

 

 

Example Question #591 : Vectors And Vector Operations

Find the Unit Normal Vector to the given plane. 

.

Possible Answers:

Correct answer:

Explanation:

Recall the definition of the Unit Normal Vector.

Let 

 

 

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