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Chapter 12: Problem 10

If \(\mathbf{v}=\left\langle v_{1}, v_{2}\right\rangle\) and \(c\) is a scalar, how do you find \(c \mathbf{v} ?\)

Short Answer

Expert verified
Answer: To find the scalar multiple of a two-dimensional vector, you need to multiply each component of the vector by the given scalar. The scalar multiple is represented as \(c\mathbf{v}\), where \(\mathbf{v}\) is the vector and c is the scalar. The resulting scalar multiple is expressed as \(\left\langle c\cdot v_{1}, c\cdot v_{2} \right\rangle\).

Step by step solution

01

Identify the vector and scalar

In this case, the given vector is \(\mathbf{v}=\left\langle v_{1}, v_{2}\right\rangle\) and the scalar is c.
02

Multiply the scalar with the components of the vector

Multiply the scalar c with each component of the vector, \(v_{1}\) and \(v_{2}\). This can be written as: \(c\mathbf{v} = \left\langle c \cdot v_{1}, c \cdot v_{2} \right\rangle\)
03

Simplify the expression (if necessary)

If the scalar and components of the vector are given numerical values, simplify the expression by calculating the products. Otherwise, the simplified expression for the scalar multiple is: \(c\mathbf{v} = \left\langle c \cdot v_{1}, c \cdot v_{2} \right\rangle\)

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