Linear Algebra : Vector-Vector Product

Example Questions

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Example Question #1 : Vector Vector Product

Compute , where

Not possible

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 #1 : Vector Vector Product

Find the vector-vector product of the following vectors.

It's not possible to multiply these vectors

Explanation:

Example Question #2 : Vector Vector Product

Calculate , given

Explanation:

By definition,

.

Example Question #1 : Vector Vector Product

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

is the projection of  onto .

lies in the same plane that contains both  and .

is a scalar.

is orthogonal to both  and .

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 .

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