Linear Algebra : Vector-Vector Product

Study concepts, example questions & explanations for Linear Algebra

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Example Questions

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Example Question #1 : Vector Vector Product

Compute , where 

Possible Answers:

Not possible

Correct answer:

Explanation:

Before we compute the product of , and , we need to check if it is possible to take the product. We will check the dimensions.  is , and  is , so the dimensions of the resulting matrix will be . Now let's compute it.

 

Example Question #2 : Vector Vector Product

Find the vector-vector product of the following vectors.

Possible Answers:

It's not possible to multiply these vectors

Correct answer:

Explanation:

Example Question #3 : Vector Vector Product

Calculate , given 

Possible Answers:

Correct answer:

Explanation:

By definition, 

.

Example Question #4 : Vector Vector Product

What is the physical significance of the resultant vector , if ?

Possible Answers:

 is orthogonal to both  and .

 is a scalar.

 lies in the same plane that contains both  and .

 is the projection of  onto .

Correct answer:

 is orthogonal to both  and .

Explanation:

By definition, the resultant cross product vector (in this case, ) is orthogonal to the original vectors that were crossed (in this case,  and ).  In , this means that  is a vector that is normal to the plane containing  and .

Example Question #5 : Vector Vector Product

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Correct answer:

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Example Question #6 : Vector Vector Product

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Example Question #1 : Vector Vector Product

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Correct answer:

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Example Question #8 : Vector Vector Product

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Correct answer:

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Example Question #9 : Vector Vector Product

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Correct answer:

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Example Question #10 : Vector Vector Product

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