The position of a vector is not important. For this reason, a vector v in standard position has initial point (0, 0) and is completely determined by its terminal point (a, b). You can represent v in component form as 〈a, b〉. Use the Pythagorean theorem to find the magnitude of v,
Problem 1 Representing a Vector
What is the component form of the vector
| Think | Write |
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| For component form, the initial point must be at the origin. You need to move it 1 unit left and 2 units down. |
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| You must move the terminal point in the same way. |
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| The new terminal point is the component form. |
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✓ Got It?
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What are the component forms of the two vectors shown here?
You can also write a vector
Problem 2 Rotating a Vector
Rotate the vector
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Step 1 Write the vector in matrix form.
Think
How can you rotate points in the coordinate plane? You can multiply by a rotation matrix.
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Step 2 Multiply the vector by the
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Step 3 The resulting vector is
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions