Calculus 3 : Cross Product

Study concepts, example questions & explanations for Calculus 3

varsity tutors app store varsity tutors android store

Example Questions

← Previous 1 3 4 5 6 7 8 9 10 11

Example Question #1 : Cross Product

Let , and .

Find .

Possible Answers:

Correct answer:

Explanation:

We are trying to find the cross product between  and .

Recall the formula for cross product.

If  , and , then

.

Now apply this to our situation.

Example Question #2 : Cross Product

Let , and .

Find .

Possible Answers:

Correct answer:

Explanation:

We are trying to find the cross product between  and .

Recall the formula for cross product.

If  , and , then

.

Now apply this to our situation.

Example Question #3 : Cross Product

True or False: The cross product can only be taken of two 3-dimensional vectors.

Possible Answers:

True

False

Correct answer:

True

Explanation:

This is true. The cross product is defined this way. The dot product however can be taken for two vectors of dimension n (provided that both vectors are the same dimension).

Example Question #3 : Cross Product

Which of the following choices is true?

Possible Answers:

Correct answer:

Explanation:

By definition, the order of the dot product of two vectors does not matter, as the final output is a scalar.  However, the cross product of two vectors will change signs depending on the order that they are crossed.  Therefore 

.

Example Question #4 : Cross Product

For what angle(s) is the cross product ?

Possible Answers:

Correct answer:

Explanation:

We have the following equation that relates the cross product of two vectors  to the relative angle between them , written as

.

From this, we can see that the numerator, or cross product, will be  whenever .  This will be true for all even multiples of .  Therefore, we find that the cross product of two vectors will be  for .

Example Question #5 : Cross Product

Evaluate

Possible Answers:

None of the other answers

Correct answer:

None of the other answers

Explanation:

It is not possible to take the cross product of -component vectors. The definition of the cross product states that the two vectors must each have components. So the above problem is impossible.

Example Question #6 : Cross Product

 Compute .

Possible Answers:

Correct answer:

Explanation:

To evaluate the cross product, we use the determinant formula

So we have

 

. (Use cofactor expansion along the top row. This is typically done when taking any cross products)

 

Example Question #7 : Cross Product

Evaluate .

Possible Answers:

None of the other answers

Correct answer:

Explanation:

To evaluate the cross product, we use the determinant formula

So we have

 

. (Use cofactor expansion along the top row. This is typically done when taking any cross products)

 

Example Question #8 : Cross Product

Find the cross product of the two vectors. 

Possible Answers:

Correct answer:

Explanation:

To find the cross product, we solve for the determinant of the matrix

The determinant equals

As the cross-product.

Example Question #10 : Cross Product

Find the cross product of the two vectors. 

Possible Answers:

Correct answer:

Explanation:

To find the cross product, we solve for the determinant of the matrix

The determinant equals

As the cross-product.

← Previous 1 3 4 5 6 7 8 9 10 11
Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: