# Precalculus : Geometric Vectors

## Example Questions

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### Example Question #171 : Matrices And Vectors

Subtract:

Explanation:

Subtract the first value of the first vector, and the second value of the first vector with the second value of the second vector.

Double negative signs are converted to a positive sign.

### Example Question #172 : Matrices And Vectors

Simplify:

Explanation:

The dimensions of the vectors are not the same.  Placeholders cannot be added to a vector.  Therefore, the values of the vectors cannot be added.

### Example Question #21 : Evaluate Geometric Vectors

Find the norm of the vector .

Explanation:

We find the norm of a vector by finding the sum of each element squared and then taking the square root.

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### Example Question #22 : Evaluate Geometric Vectors

Find the norm of the vector .

Explanation:

We find the norm of a vector by finding the sum of each component squared and then taking the square root of that sum.

### Example Question #23 : Evaluate Geometric Vectors

Find the norm of the vector:

Explanation:

The norm of a vector is also known as the length of the vector. The norm is given by the formula:

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Here, we have

,

### Example Question #24 : Evaluate Geometric Vectors

Find the norm of vector .

Explanation:

Write the formula to find the norm, or the length the vector.

Substitute the known values of the vector and solve.

### Example Question #25 : Evaluate Geometric Vectors

Find the norm (magnitude) of the following vector:

Explanation:

Use the following equation to find the magnitude of a vector:

In this case we have:

So plug in our values:

So:

### Example Question #26 : Evaluate Geometric Vectors

Find the product of the vector  and the scalar .