# Precalculus : Geometric Vectors

## Example Questions

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### Example Question #171 : Matrices And Vectors

Subtract: Possible Answers:     Correct answer: 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: Possible Answers:     Correct answer: 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.

The correct answer is: ### Example Question #21 : Evaluate Geometric Vectors

Find the norm of the vector .

Possible Answers:    Correct answer: Explanation:

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

### Example Question #22 : Evaluate Geometric Vectors

Find the norm of the vector .

Possible Answers:    Correct answer: 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: Possible Answers:     Correct answer: Explanation:

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

Here, we have ,

the correct answer.

### Example Question #24 : Evaluate Geometric Vectors

Find the norm of vector .

Possible Answers:     Correct answer: 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: Possible Answers:     Correct answer: 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 .

Possible Answers:    Correct answer: Explanation:

When multiplying a vector by a scalar we multiply each component of the vector by the scalar and the result is a vector: 1 3 Next →

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