### All Linear Algebra Resources

## Example Questions

### Example Question #1 : Vector Vector Product

Compute , where

**Possible Answers:**

Not possible

**Correct answer:**

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:**

### Example Question #3 : Vector Vector Product

Calculate , given

**Possible Answers:**

**Correct answer:**

By definition,

.

### Example Question #4 : Vector Vector Product

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

**Possible Answers:**

is the projection of onto .

lies in the same plane that contains both and .

is a scalar.

is orthogonal to both and .

**Correct answer:**

is orthogonal to both and .

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

**Possible Answers:**

**Correct answer:**

### Example Question #6 : Vector Vector Product

**Possible Answers:**

**Correct answer:**

### Example Question #7 : Vector Vector Product

**Possible Answers:**

**Correct answer:**

### Example Question #8 : Vector Vector Product

**Possible Answers:**

**Correct answer:**

### Example Question #9 : Vector Vector Product

**Possible Answers:**

**Correct answer:**

### Example Question #10 : Vector Vector Product

**Possible Answers:**

**Correct answer:**

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