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The Humongous Book of Trigonometry Problems by W. Michael Kelley

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Scalar Multiplication

Calculate c <a, b>

15.21 Express c<a,b> in component form, assuming a, b, and c are real numbers.

The vector <a,b> is multiplied by a real number c; that real number is called a scalar. To multiply a vector in component form by a scalar value, multiply each of the components by the scalar. In this example, multiply both a and b by c.

A vector has a value (magnitude) and a direction. A scalar only has a value. However, that value changes the SCALE of the vector. For example, multiplying a vector by the scalar 2 doubles its length.

c<a,b> = <ca, cb>

15.22 Express the vector in component form: 3<4,7>.

Multiply each of the components of vector <4,7> by 3.

15.23 Express the vector in component form: –5<–1,8>.

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